Infinite integrals involving Bessel functions by an improved approach of contour integration and the residue theorem
Abstract Two lemmas are established to evaluate integrals involving Bessel functions or products of two Bessel functions on a large semicircle. These lemmas are as useful as Jordan’s lemma. With the help of them, the approach of contour integration and residue theorem to infinite integrals becomes m...
Ausführliche Beschreibung
Gespeichert in:
| Autor*in: |
Lin, Qiong-Gui [verfasserIn] |
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| Format: |
E-Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2014 |
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| Schlagwörter: |
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| Übergeordnetes Werk: |
Enthalten in: The Ramanujan journal - Dordrecht [u.a.] : Springer Science + Business Media B.V, 1997, 35(2014), 3 vom: 22. Jan., Seite 443-466 |
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| Übergeordnetes Werk: |
volume:35 ; year:2014 ; number:3 ; day:22 ; month:01 ; pages:443-466 |
| Links: |
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| DOI / URN: |
10.1007/s11139-013-9529-4 |
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| Katalog-ID: |
SPR017031931 |
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| 520 | |a Abstract Two lemmas are established to evaluate integrals involving Bessel functions or products of two Bessel functions on a large semicircle. These lemmas are as useful as Jordan’s lemma. With the help of them, the approach of contour integration and residue theorem to infinite integrals becomes much more powerful than ever before, yet is still simple and easy. A general formula is derived for infinite integrals involving rational functions, powers and Bessel functions, the index of the power and the order of the Bessel function being independent, and the result is expressed in terms of residues and coefficients of the Laurent series of the rational function. Similar formulae are presented for infinite integrals involving Neumann or Struve functions. Another general formula is derived for infinite integrals involving rational functions, powers and two Bessel functions, the index of the power and the orders of the Bessel functions being independent. The formulation presented may be extended to infinite integrals of similar types. Typical examples are worked out for each type of integral, and many of the results obtained seem not available in the literature. | ||
| 650 | 4 | |a Infinite integrals |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a Bessel functions |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a Contour integration |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a Residue theorem |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a Neumann functions |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a Struve functions |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a Hankel transform |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a Mellin transform |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a -Transform |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a -Transform |7 (dpeaa)DE-He213 | |
| 773 | 0 | 8 | |i Enthalten in |t The Ramanujan journal |d Dordrecht [u.a.] : Springer Science + Business Media B.V, 1997 |g 35(2014), 3 vom: 22. Jan., Seite 443-466 |w (DE-627)320521133 |w (DE-600)2014600-0 |x 1572-9303 |7 nnns |
| 773 | 1 | 8 | |g volume:35 |g year:2014 |g number:3 |g day:22 |g month:01 |g pages:443-466 |
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10.1007/s11139-013-9529-4 doi (DE-627)SPR017031931 (SPR)s11139-013-9529-4-e DE-627 ger DE-627 rakwb eng 510 ASE 31.00 bkl Lin, Qiong-Gui verfasserin aut Infinite integrals involving Bessel functions by an improved approach of contour integration and the residue theorem 2014 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract Two lemmas are established to evaluate integrals involving Bessel functions or products of two Bessel functions on a large semicircle. These lemmas are as useful as Jordan’s lemma. With the help of them, the approach of contour integration and residue theorem to infinite integrals becomes much more powerful than ever before, yet is still simple and easy. A general formula is derived for infinite integrals involving rational functions, powers and Bessel functions, the index of the power and the order of the Bessel function being independent, and the result is expressed in terms of residues and coefficients of the Laurent series of the rational function. Similar formulae are presented for infinite integrals involving Neumann or Struve functions. Another general formula is derived for infinite integrals involving rational functions, powers and two Bessel functions, the index of the power and the orders of the Bessel functions being independent. The formulation presented may be extended to infinite integrals of similar types. Typical examples are worked out for each type of integral, and many of the results obtained seem not available in the literature. Infinite integrals (dpeaa)DE-He213 Bessel functions (dpeaa)DE-He213 Contour integration (dpeaa)DE-He213 Residue theorem (dpeaa)DE-He213 Neumann functions (dpeaa)DE-He213 Struve functions (dpeaa)DE-He213 Hankel transform (dpeaa)DE-He213 Mellin transform (dpeaa)DE-He213 -Transform (dpeaa)DE-He213 -Transform (dpeaa)DE-He213 Enthalten in The Ramanujan journal Dordrecht [u.a.] : Springer Science + Business Media B.V, 1997 35(2014), 3 vom: 22. Jan., Seite 443-466 (DE-627)320521133 (DE-600)2014600-0 1572-9303 nnns volume:35 year:2014 number:3 day:22 month:01 pages:443-466 https://dx.doi.org/10.1007/s11139-013-9529-4 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER SSG-OPC-MAT SSG-OPC-ASE GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 31.00 ASE AR 35 2014 3 22 01 443-466 |
| spelling |
10.1007/s11139-013-9529-4 doi (DE-627)SPR017031931 (SPR)s11139-013-9529-4-e DE-627 ger DE-627 rakwb eng 510 ASE 31.00 bkl Lin, Qiong-Gui verfasserin aut Infinite integrals involving Bessel functions by an improved approach of contour integration and the residue theorem 2014 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract Two lemmas are established to evaluate integrals involving Bessel functions or products of two Bessel functions on a large semicircle. These lemmas are as useful as Jordan’s lemma. With the help of them, the approach of contour integration and residue theorem to infinite integrals becomes much more powerful than ever before, yet is still simple and easy. A general formula is derived for infinite integrals involving rational functions, powers and Bessel functions, the index of the power and the order of the Bessel function being independent, and the result is expressed in terms of residues and coefficients of the Laurent series of the rational function. Similar formulae are presented for infinite integrals involving Neumann or Struve functions. Another general formula is derived for infinite integrals involving rational functions, powers and two Bessel functions, the index of the power and the orders of the Bessel functions being independent. The formulation presented may be extended to infinite integrals of similar types. Typical examples are worked out for each type of integral, and many of the results obtained seem not available in the literature. Infinite integrals (dpeaa)DE-He213 Bessel functions (dpeaa)DE-He213 Contour integration (dpeaa)DE-He213 Residue theorem (dpeaa)DE-He213 Neumann functions (dpeaa)DE-He213 Struve functions (dpeaa)DE-He213 Hankel transform (dpeaa)DE-He213 Mellin transform (dpeaa)DE-He213 -Transform (dpeaa)DE-He213 -Transform (dpeaa)DE-He213 Enthalten in The Ramanujan journal Dordrecht [u.a.] : Springer Science + Business Media B.V, 1997 35(2014), 3 vom: 22. Jan., Seite 443-466 (DE-627)320521133 (DE-600)2014600-0 1572-9303 nnns volume:35 year:2014 number:3 day:22 month:01 pages:443-466 https://dx.doi.org/10.1007/s11139-013-9529-4 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER SSG-OPC-MAT SSG-OPC-ASE GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 31.00 ASE AR 35 2014 3 22 01 443-466 |
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10.1007/s11139-013-9529-4 doi (DE-627)SPR017031931 (SPR)s11139-013-9529-4-e DE-627 ger DE-627 rakwb eng 510 ASE 31.00 bkl Lin, Qiong-Gui verfasserin aut Infinite integrals involving Bessel functions by an improved approach of contour integration and the residue theorem 2014 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract Two lemmas are established to evaluate integrals involving Bessel functions or products of two Bessel functions on a large semicircle. These lemmas are as useful as Jordan’s lemma. With the help of them, the approach of contour integration and residue theorem to infinite integrals becomes much more powerful than ever before, yet is still simple and easy. A general formula is derived for infinite integrals involving rational functions, powers and Bessel functions, the index of the power and the order of the Bessel function being independent, and the result is expressed in terms of residues and coefficients of the Laurent series of the rational function. Similar formulae are presented for infinite integrals involving Neumann or Struve functions. Another general formula is derived for infinite integrals involving rational functions, powers and two Bessel functions, the index of the power and the orders of the Bessel functions being independent. The formulation presented may be extended to infinite integrals of similar types. Typical examples are worked out for each type of integral, and many of the results obtained seem not available in the literature. Infinite integrals (dpeaa)DE-He213 Bessel functions (dpeaa)DE-He213 Contour integration (dpeaa)DE-He213 Residue theorem (dpeaa)DE-He213 Neumann functions (dpeaa)DE-He213 Struve functions (dpeaa)DE-He213 Hankel transform (dpeaa)DE-He213 Mellin transform (dpeaa)DE-He213 -Transform (dpeaa)DE-He213 -Transform (dpeaa)DE-He213 Enthalten in The Ramanujan journal Dordrecht [u.a.] : Springer Science + Business Media B.V, 1997 35(2014), 3 vom: 22. Jan., Seite 443-466 (DE-627)320521133 (DE-600)2014600-0 1572-9303 nnns volume:35 year:2014 number:3 day:22 month:01 pages:443-466 https://dx.doi.org/10.1007/s11139-013-9529-4 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER SSG-OPC-MAT SSG-OPC-ASE GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 31.00 ASE AR 35 2014 3 22 01 443-466 |
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10.1007/s11139-013-9529-4 doi (DE-627)SPR017031931 (SPR)s11139-013-9529-4-e DE-627 ger DE-627 rakwb eng 510 ASE 31.00 bkl Lin, Qiong-Gui verfasserin aut Infinite integrals involving Bessel functions by an improved approach of contour integration and the residue theorem 2014 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract Two lemmas are established to evaluate integrals involving Bessel functions or products of two Bessel functions on a large semicircle. These lemmas are as useful as Jordan’s lemma. With the help of them, the approach of contour integration and residue theorem to infinite integrals becomes much more powerful than ever before, yet is still simple and easy. A general formula is derived for infinite integrals involving rational functions, powers and Bessel functions, the index of the power and the order of the Bessel function being independent, and the result is expressed in terms of residues and coefficients of the Laurent series of the rational function. Similar formulae are presented for infinite integrals involving Neumann or Struve functions. Another general formula is derived for infinite integrals involving rational functions, powers and two Bessel functions, the index of the power and the orders of the Bessel functions being independent. The formulation presented may be extended to infinite integrals of similar types. Typical examples are worked out for each type of integral, and many of the results obtained seem not available in the literature. Infinite integrals (dpeaa)DE-He213 Bessel functions (dpeaa)DE-He213 Contour integration (dpeaa)DE-He213 Residue theorem (dpeaa)DE-He213 Neumann functions (dpeaa)DE-He213 Struve functions (dpeaa)DE-He213 Hankel transform (dpeaa)DE-He213 Mellin transform (dpeaa)DE-He213 -Transform (dpeaa)DE-He213 -Transform (dpeaa)DE-He213 Enthalten in The Ramanujan journal Dordrecht [u.a.] : Springer Science + Business Media B.V, 1997 35(2014), 3 vom: 22. Jan., Seite 443-466 (DE-627)320521133 (DE-600)2014600-0 1572-9303 nnns volume:35 year:2014 number:3 day:22 month:01 pages:443-466 https://dx.doi.org/10.1007/s11139-013-9529-4 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER SSG-OPC-MAT SSG-OPC-ASE GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 31.00 ASE AR 35 2014 3 22 01 443-466 |
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10.1007/s11139-013-9529-4 doi (DE-627)SPR017031931 (SPR)s11139-013-9529-4-e DE-627 ger DE-627 rakwb eng 510 ASE 31.00 bkl Lin, Qiong-Gui verfasserin aut Infinite integrals involving Bessel functions by an improved approach of contour integration and the residue theorem 2014 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract Two lemmas are established to evaluate integrals involving Bessel functions or products of two Bessel functions on a large semicircle. These lemmas are as useful as Jordan’s lemma. With the help of them, the approach of contour integration and residue theorem to infinite integrals becomes much more powerful than ever before, yet is still simple and easy. A general formula is derived for infinite integrals involving rational functions, powers and Bessel functions, the index of the power and the order of the Bessel function being independent, and the result is expressed in terms of residues and coefficients of the Laurent series of the rational function. Similar formulae are presented for infinite integrals involving Neumann or Struve functions. Another general formula is derived for infinite integrals involving rational functions, powers and two Bessel functions, the index of the power and the orders of the Bessel functions being independent. The formulation presented may be extended to infinite integrals of similar types. Typical examples are worked out for each type of integral, and many of the results obtained seem not available in the literature. Infinite integrals (dpeaa)DE-He213 Bessel functions (dpeaa)DE-He213 Contour integration (dpeaa)DE-He213 Residue theorem (dpeaa)DE-He213 Neumann functions (dpeaa)DE-He213 Struve functions (dpeaa)DE-He213 Hankel transform (dpeaa)DE-He213 Mellin transform (dpeaa)DE-He213 -Transform (dpeaa)DE-He213 -Transform (dpeaa)DE-He213 Enthalten in The Ramanujan journal Dordrecht [u.a.] : Springer Science + Business Media B.V, 1997 35(2014), 3 vom: 22. Jan., Seite 443-466 (DE-627)320521133 (DE-600)2014600-0 1572-9303 nnns volume:35 year:2014 number:3 day:22 month:01 pages:443-466 https://dx.doi.org/10.1007/s11139-013-9529-4 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER SSG-OPC-MAT SSG-OPC-ASE GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 31.00 ASE AR 35 2014 3 22 01 443-466 |
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These lemmas are as useful as Jordan’s lemma. With the help of them, the approach of contour integration and residue theorem to infinite integrals becomes much more powerful than ever before, yet is still simple and easy. A general formula is derived for infinite integrals involving rational functions, powers and Bessel functions, the index of the power and the order of the Bessel function being independent, and the result is expressed in terms of residues and coefficients of the Laurent series of the rational function. Similar formulae are presented for infinite integrals involving Neumann or Struve functions. Another general formula is derived for infinite integrals involving rational functions, powers and two Bessel functions, the index of the power and the orders of the Bessel functions being independent. The formulation presented may be extended to infinite integrals of similar types. Typical examples are worked out for each type of integral, and many of the results obtained seem not available in the literature.</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Infinite integrals</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Bessel functions</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Contour integration</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Residue theorem</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Neumann functions</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Struve functions</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Hankel transform</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Mellin transform</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">-Transform</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">-Transform</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="773" ind1="0" ind2="8"><subfield code="i">Enthalten in</subfield><subfield code="t">The Ramanujan journal</subfield><subfield code="d">Dordrecht [u.a.] : Springer Science + Business Media B.V, 1997</subfield><subfield code="g">35(2014), 3 vom: 22. 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Lin, Qiong-Gui |
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Lin, Qiong-Gui ddc 510 bkl 31.00 misc Infinite integrals misc Bessel functions misc Contour integration misc Residue theorem misc Neumann functions misc Struve functions misc Hankel transform misc Mellin transform misc -Transform Infinite integrals involving Bessel functions by an improved approach of contour integration and the residue theorem |
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510 ASE 31.00 bkl Infinite integrals involving Bessel functions by an improved approach of contour integration and the residue theorem Infinite integrals (dpeaa)DE-He213 Bessel functions (dpeaa)DE-He213 Contour integration (dpeaa)DE-He213 Residue theorem (dpeaa)DE-He213 Neumann functions (dpeaa)DE-He213 Struve functions (dpeaa)DE-He213 Hankel transform (dpeaa)DE-He213 Mellin transform (dpeaa)DE-He213 -Transform (dpeaa)DE-He213 |
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ddc 510 bkl 31.00 misc Infinite integrals misc Bessel functions misc Contour integration misc Residue theorem misc Neumann functions misc Struve functions misc Hankel transform misc Mellin transform misc -Transform |
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ddc 510 bkl 31.00 misc Infinite integrals misc Bessel functions misc Contour integration misc Residue theorem misc Neumann functions misc Struve functions misc Hankel transform misc Mellin transform misc -Transform |
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Infinite integrals involving Bessel functions by an improved approach of contour integration and the residue theorem |
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Infinite integrals involving Bessel functions by an improved approach of contour integration and the residue theorem |
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infinite integrals involving bessel functions by an improved approach of contour integration and the residue theorem |
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Infinite integrals involving Bessel functions by an improved approach of contour integration and the residue theorem |
| abstract |
Abstract Two lemmas are established to evaluate integrals involving Bessel functions or products of two Bessel functions on a large semicircle. These lemmas are as useful as Jordan’s lemma. With the help of them, the approach of contour integration and residue theorem to infinite integrals becomes much more powerful than ever before, yet is still simple and easy. A general formula is derived for infinite integrals involving rational functions, powers and Bessel functions, the index of the power and the order of the Bessel function being independent, and the result is expressed in terms of residues and coefficients of the Laurent series of the rational function. Similar formulae are presented for infinite integrals involving Neumann or Struve functions. Another general formula is derived for infinite integrals involving rational functions, powers and two Bessel functions, the index of the power and the orders of the Bessel functions being independent. The formulation presented may be extended to infinite integrals of similar types. Typical examples are worked out for each type of integral, and many of the results obtained seem not available in the literature. |
| abstractGer |
Abstract Two lemmas are established to evaluate integrals involving Bessel functions or products of two Bessel functions on a large semicircle. These lemmas are as useful as Jordan’s lemma. With the help of them, the approach of contour integration and residue theorem to infinite integrals becomes much more powerful than ever before, yet is still simple and easy. A general formula is derived for infinite integrals involving rational functions, powers and Bessel functions, the index of the power and the order of the Bessel function being independent, and the result is expressed in terms of residues and coefficients of the Laurent series of the rational function. Similar formulae are presented for infinite integrals involving Neumann or Struve functions. Another general formula is derived for infinite integrals involving rational functions, powers and two Bessel functions, the index of the power and the orders of the Bessel functions being independent. The formulation presented may be extended to infinite integrals of similar types. Typical examples are worked out for each type of integral, and many of the results obtained seem not available in the literature. |
| abstract_unstemmed |
Abstract Two lemmas are established to evaluate integrals involving Bessel functions or products of two Bessel functions on a large semicircle. These lemmas are as useful as Jordan’s lemma. With the help of them, the approach of contour integration and residue theorem to infinite integrals becomes much more powerful than ever before, yet is still simple and easy. A general formula is derived for infinite integrals involving rational functions, powers and Bessel functions, the index of the power and the order of the Bessel function being independent, and the result is expressed in terms of residues and coefficients of the Laurent series of the rational function. Similar formulae are presented for infinite integrals involving Neumann or Struve functions. Another general formula is derived for infinite integrals involving rational functions, powers and two Bessel functions, the index of the power and the orders of the Bessel functions being independent. The formulation presented may be extended to infinite integrals of similar types. Typical examples are worked out for each type of integral, and many of the results obtained seem not available in the literature. |
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| container_issue |
3 |
| title_short |
Infinite integrals involving Bessel functions by an improved approach of contour integration and the residue theorem |
| url |
https://dx.doi.org/10.1007/s11139-013-9529-4 |
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| doi_str |
10.1007/s11139-013-9529-4 |
| up_date |
2024-07-04T01:56:59.196Z |
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| score |
7.4009037 |