On Bernstein's inequality for ultraspherical polynomials
Abstract. We prove the following inequality for the ultraspherical polynomials $ P_n^ {(\lambda )} $ :¶¶ $ (\sin (\mit\Theta ))^\lambda |P_n^{(\lambda )}(\cos (\mit\Theta )) | \le {{2^{1-\lambda }}\over {\mit\Gamma (\lambda )} } { {\mit\Gamma (n+ {{3}\over {2}} \lambda )}\over {\mit\Gamma (n+1+ {{1}...
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| Autor*in: |
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| Format: |
E-Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
1997 |
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| Umfang: |
4 |
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| Reproduktion: |
Springer Online Journal Archives 1860-2002 |
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| Übergeordnetes Werk: |
in: Archiv der Mathematik - 1948, 69(1997) vom: Juni, Seite 487-490 |
| Übergeordnetes Werk: |
volume:69 ; year:1997 ; month:06 ; pages:487-490 ; extent:4 |
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| 520 | |a Abstract. We prove the following inequality for the ultraspherical polynomials $ P_n^ {(\lambda )} $ :¶¶ $ (\sin (\mit\Theta ))^\lambda |P_n^{(\lambda )}(\cos (\mit\Theta )) | \le {{2^{1-\lambda }}\over {\mit\Gamma (\lambda )} } { {\mit\Gamma (n+ {{3}\over {2}} \lambda )}\over {\mit\Gamma (n+1+ {{1} \over {2}}\lambda )}}, $(*) ¶¶ where $0 \le \lambda \le 1, n \ge 0$ , and $0 \le {\mit\Theta} \le \pi $ . Inequality (*) refines results given by S. Bernstein, L. Lorch, and A. Laforgia. | ||
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(DE-627)NLEJ18905462X DE-627 ger DE-627 rakwb eng On Bernstein's inequality for ultraspherical polynomials 1997 4 nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier Abstract. We prove the following inequality for the ultraspherical polynomials $ P_n^ {(\lambda )} $ :¶¶ $ (\sin (\mit\Theta ))^\lambda |P_n^{(\lambda )}(\cos (\mit\Theta )) | \le {{2^{1-\lambda }}\over {\mit\Gamma (\lambda )} } { {\mit\Gamma (n+ {{3}\over {2}} \lambda )}\over {\mit\Gamma (n+1+ {{1} \over {2}}\lambda )}}, $(*) ¶¶ where $0 \le \lambda \le 1, n \ge 0$ , and $0 \le {\mit\Theta} \le \pi $ . Inequality (*) refines results given by S. Bernstein, L. Lorch, and A. Laforgia. Springer Online Journal Archives 1860-2002 Alzer, Horst oth in Archiv der Mathematik 1948 69(1997) vom: Juni, Seite 487-490 (DE-627)NLEJ18899193X (DE-600)1458441-4 1420-8938 nnns volume:69 year:1997 month:06 pages:487-490 extent:4 http://dx.doi.org/10.1007/s000130050150 GBV_USEFLAG_U ZDB-1-SOJ GBV_NL_ARTICLE AR 69 1997 6 487-490 4 |
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(DE-627)NLEJ18905462X DE-627 ger DE-627 rakwb eng On Bernstein's inequality for ultraspherical polynomials 1997 4 nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier Abstract. We prove the following inequality for the ultraspherical polynomials $ P_n^ {(\lambda )} $ :¶¶ $ (\sin (\mit\Theta ))^\lambda |P_n^{(\lambda )}(\cos (\mit\Theta )) | \le {{2^{1-\lambda }}\over {\mit\Gamma (\lambda )} } { {\mit\Gamma (n+ {{3}\over {2}} \lambda )}\over {\mit\Gamma (n+1+ {{1} \over {2}}\lambda )}}, $(*) ¶¶ where $0 \le \lambda \le 1, n \ge 0$ , and $0 \le {\mit\Theta} \le \pi $ . Inequality (*) refines results given by S. Bernstein, L. Lorch, and A. Laforgia. Springer Online Journal Archives 1860-2002 Alzer, Horst oth in Archiv der Mathematik 1948 69(1997) vom: Juni, Seite 487-490 (DE-627)NLEJ18899193X (DE-600)1458441-4 1420-8938 nnns volume:69 year:1997 month:06 pages:487-490 extent:4 http://dx.doi.org/10.1007/s000130050150 GBV_USEFLAG_U ZDB-1-SOJ GBV_NL_ARTICLE AR 69 1997 6 487-490 4 |
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(DE-627)NLEJ18905462X DE-627 ger DE-627 rakwb eng On Bernstein's inequality for ultraspherical polynomials 1997 4 nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier Abstract. We prove the following inequality for the ultraspherical polynomials $ P_n^ {(\lambda )} $ :¶¶ $ (\sin (\mit\Theta ))^\lambda |P_n^{(\lambda )}(\cos (\mit\Theta )) | \le {{2^{1-\lambda }}\over {\mit\Gamma (\lambda )} } { {\mit\Gamma (n+ {{3}\over {2}} \lambda )}\over {\mit\Gamma (n+1+ {{1} \over {2}}\lambda )}}, $(*) ¶¶ where $0 \le \lambda \le 1, n \ge 0$ , and $0 \le {\mit\Theta} \le \pi $ . Inequality (*) refines results given by S. Bernstein, L. Lorch, and A. Laforgia. Springer Online Journal Archives 1860-2002 Alzer, Horst oth in Archiv der Mathematik 1948 69(1997) vom: Juni, Seite 487-490 (DE-627)NLEJ18899193X (DE-600)1458441-4 1420-8938 nnns volume:69 year:1997 month:06 pages:487-490 extent:4 http://dx.doi.org/10.1007/s000130050150 GBV_USEFLAG_U ZDB-1-SOJ GBV_NL_ARTICLE AR 69 1997 6 487-490 4 |
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(DE-627)NLEJ18905462X DE-627 ger DE-627 rakwb eng On Bernstein's inequality for ultraspherical polynomials 1997 4 nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier Abstract. We prove the following inequality for the ultraspherical polynomials $ P_n^ {(\lambda )} $ :¶¶ $ (\sin (\mit\Theta ))^\lambda |P_n^{(\lambda )}(\cos (\mit\Theta )) | \le {{2^{1-\lambda }}\over {\mit\Gamma (\lambda )} } { {\mit\Gamma (n+ {{3}\over {2}} \lambda )}\over {\mit\Gamma (n+1+ {{1} \over {2}}\lambda )}}, $(*) ¶¶ where $0 \le \lambda \le 1, n \ge 0$ , and $0 \le {\mit\Theta} \le \pi $ . Inequality (*) refines results given by S. Bernstein, L. Lorch, and A. Laforgia. Springer Online Journal Archives 1860-2002 Alzer, Horst oth in Archiv der Mathematik 1948 69(1997) vom: Juni, Seite 487-490 (DE-627)NLEJ18899193X (DE-600)1458441-4 1420-8938 nnns volume:69 year:1997 month:06 pages:487-490 extent:4 http://dx.doi.org/10.1007/s000130050150 GBV_USEFLAG_U ZDB-1-SOJ GBV_NL_ARTICLE AR 69 1997 6 487-490 4 |
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(DE-627)NLEJ18905462X DE-627 ger DE-627 rakwb eng On Bernstein's inequality for ultraspherical polynomials 1997 4 nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier Abstract. We prove the following inequality for the ultraspherical polynomials $ P_n^ {(\lambda )} $ :¶¶ $ (\sin (\mit\Theta ))^\lambda |P_n^{(\lambda )}(\cos (\mit\Theta )) | \le {{2^{1-\lambda }}\over {\mit\Gamma (\lambda )} } { {\mit\Gamma (n+ {{3}\over {2}} \lambda )}\over {\mit\Gamma (n+1+ {{1} \over {2}}\lambda )}}, $(*) ¶¶ where $0 \le \lambda \le 1, n \ge 0$ , and $0 \le {\mit\Theta} \le \pi $ . Inequality (*) refines results given by S. Bernstein, L. Lorch, and A. Laforgia. Springer Online Journal Archives 1860-2002 Alzer, Horst oth in Archiv der Mathematik 1948 69(1997) vom: Juni, Seite 487-490 (DE-627)NLEJ18899193X (DE-600)1458441-4 1420-8938 nnns volume:69 year:1997 month:06 pages:487-490 extent:4 http://dx.doi.org/10.1007/s000130050150 GBV_USEFLAG_U ZDB-1-SOJ GBV_NL_ARTICLE AR 69 1997 6 487-490 4 |
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Abstract. We prove the following inequality for the ultraspherical polynomials $ P_n^ {(\lambda )} $ :¶¶ $ (\sin (\mit\Theta ))^\lambda |P_n^{(\lambda )}(\cos (\mit\Theta )) | \le {{2^{1-\lambda }}\over {\mit\Gamma (\lambda )} } { {\mit\Gamma (n+ {{3}\over {2}} \lambda )}\over {\mit\Gamma (n+1+ {{1} \over {2}}\lambda )}}, $(*) ¶¶ where $0 \le \lambda \le 1, n \ge 0$ , and $0 \le {\mit\Theta} \le \pi $ . Inequality (*) refines results given by S. Bernstein, L. Lorch, and A. Laforgia. |
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Abstract. We prove the following inequality for the ultraspherical polynomials $ P_n^ {(\lambda )} $ :¶¶ $ (\sin (\mit\Theta ))^\lambda |P_n^{(\lambda )}(\cos (\mit\Theta )) | \le {{2^{1-\lambda }}\over {\mit\Gamma (\lambda )} } { {\mit\Gamma (n+ {{3}\over {2}} \lambda )}\over {\mit\Gamma (n+1+ {{1} \over {2}}\lambda )}}, $(*) ¶¶ where $0 \le \lambda \le 1, n \ge 0$ , and $0 \le {\mit\Theta} \le \pi $ . Inequality (*) refines results given by S. Bernstein, L. Lorch, and A. Laforgia. |
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Abstract. We prove the following inequality for the ultraspherical polynomials $ P_n^ {(\lambda )} $ :¶¶ $ (\sin (\mit\Theta ))^\lambda |P_n^{(\lambda )}(\cos (\mit\Theta )) | \le {{2^{1-\lambda }}\over {\mit\Gamma (\lambda )} } { {\mit\Gamma (n+ {{3}\over {2}} \lambda )}\over {\mit\Gamma (n+1+ {{1} \over {2}}\lambda )}}, $(*) ¶¶ where $0 \le \lambda \le 1, n \ge 0$ , and $0 \le {\mit\Theta} \le \pi $ . Inequality (*) refines results given by S. Bernstein, L. Lorch, and A. Laforgia. |
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