Some supercongruences occurring in truncated hypergeometric series
For the purposes of this paper supercongruences are congruences between terminating hypergeometric series and quotients of p-adic Gamma functions that are stronger than those one can expect to prove using commutative formal group laws. We prove a number of such supercongruences by using classical hy...
Ausführliche Beschreibung
Autor*in: |
Long, Ling [verfasserIn] |
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Format: |
E-Artikel |
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Sprache: |
Englisch |
Erschienen: |
2016transfer abstract |
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Umfang: |
36 |
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Übergeordnetes Werk: |
Enthalten in: Evidence of Titan’s climate history from evaporite distribution - MacKenzie, Shannon M. ELSEVIER, 2014, Amsterdam [u.a.] |
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Übergeordnetes Werk: |
volume:290 ; year:2016 ; day:26 ; month:02 ; pages:773-808 ; extent:36 |
Links: |
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DOI / URN: |
10.1016/j.aim.2015.11.043 |
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ELV035552050 |
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520 | |a For the purposes of this paper supercongruences are congruences between terminating hypergeometric series and quotients of p-adic Gamma functions that are stronger than those one can expect to prove using commutative formal group laws. We prove a number of such supercongruences by using classical hypergeometric transformation formulae. These formulae, most of which are decades or centuries old, allow us to write the terminating series as the ratio of products of Γ-values. At this point sums have become quotients. Writing these Γ-quotients as Γ p -quotients, we are in a situation that is well-suited for proving p-adic congruences. These Γ p -functions can be p-adically approximated by their Taylor series expansions. Sometimes there is cancellation of the lower order terms, leading to stronger congruences. Using this technique we prove, among other things, a conjecture of Kibelbek and a strengthened version of a conjecture of van Hamme. | ||
520 | |a For the purposes of this paper supercongruences are congruences between terminating hypergeometric series and quotients of p-adic Gamma functions that are stronger than those one can expect to prove using commutative formal group laws. We prove a number of such supercongruences by using classical hypergeometric transformation formulae. These formulae, most of which are decades or centuries old, allow us to write the terminating series as the ratio of products of Γ-values. At this point sums have become quotients. Writing these Γ-quotients as Γ p -quotients, we are in a situation that is well-suited for proving p-adic congruences. These Γ p -functions can be p-adically approximated by their Taylor series expansions. Sometimes there is cancellation of the lower order terms, leading to stronger congruences. Using this technique we prove, among other things, a conjecture of Kibelbek and a strengthened version of a conjecture of van Hamme. | ||
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10.1016/j.aim.2015.11.043 doi GBVA2016020000011.pica (DE-627)ELV035552050 (ELSEVIER)S0001-8708(15)00521-6 DE-627 ger DE-627 rakwb eng 510 510 DE-600 520 VZ 530 VZ 570 VZ BIODIV DE-30 fid 44.94 bkl Long, Ling verfasserin aut Some supercongruences occurring in truncated hypergeometric series 2016transfer abstract 36 nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier For the purposes of this paper supercongruences are congruences between terminating hypergeometric series and quotients of p-adic Gamma functions that are stronger than those one can expect to prove using commutative formal group laws. We prove a number of such supercongruences by using classical hypergeometric transformation formulae. These formulae, most of which are decades or centuries old, allow us to write the terminating series as the ratio of products of Γ-values. At this point sums have become quotients. Writing these Γ-quotients as Γ p -quotients, we are in a situation that is well-suited for proving p-adic congruences. These Γ p -functions can be p-adically approximated by their Taylor series expansions. Sometimes there is cancellation of the lower order terms, leading to stronger congruences. Using this technique we prove, among other things, a conjecture of Kibelbek and a strengthened version of a conjecture of van Hamme. For the purposes of this paper supercongruences are congruences between terminating hypergeometric series and quotients of p-adic Gamma functions that are stronger than those one can expect to prove using commutative formal group laws. We prove a number of such supercongruences by using classical hypergeometric transformation formulae. These formulae, most of which are decades or centuries old, allow us to write the terminating series as the ratio of products of Γ-values. At this point sums have become quotients. Writing these Γ-quotients as Γ p -quotients, we are in a situation that is well-suited for proving p-adic congruences. These Γ p -functions can be p-adically approximated by their Taylor series expansions. Sometimes there is cancellation of the lower order terms, leading to stronger congruences. Using this technique we prove, among other things, a conjecture of Kibelbek and a strengthened version of a conjecture of van Hamme. Hypergeometric series Elsevier Supercongruences Elsevier p-adic Gamma functions Elsevier Ramakrishna, Ravi oth Enthalten in Elsevier MacKenzie, Shannon M. ELSEVIER Evidence of Titan’s climate history from evaporite distribution 2014 Amsterdam [u.a.] (DE-627)ELV012586625 volume:290 year:2016 day:26 month:02 pages:773-808 extent:36 https://doi.org/10.1016/j.aim.2015.11.043 Volltext GBV_USEFLAG_U GBV_ELV SYSFLAG_U FID-BIODIV SSG-OLC-PHA GBV_ILN_22 GBV_ILN_359 44.94 Hals-Nasen-Ohrenheilkunde VZ AR 290 2016 26 0226 773-808 36 045F 510 |
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10.1016/j.aim.2015.11.043 doi GBVA2016020000011.pica (DE-627)ELV035552050 (ELSEVIER)S0001-8708(15)00521-6 DE-627 ger DE-627 rakwb eng 510 510 DE-600 520 VZ 530 VZ 570 VZ BIODIV DE-30 fid 44.94 bkl Long, Ling verfasserin aut Some supercongruences occurring in truncated hypergeometric series 2016transfer abstract 36 nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier For the purposes of this paper supercongruences are congruences between terminating hypergeometric series and quotients of p-adic Gamma functions that are stronger than those one can expect to prove using commutative formal group laws. We prove a number of such supercongruences by using classical hypergeometric transformation formulae. These formulae, most of which are decades or centuries old, allow us to write the terminating series as the ratio of products of Γ-values. At this point sums have become quotients. Writing these Γ-quotients as Γ p -quotients, we are in a situation that is well-suited for proving p-adic congruences. These Γ p -functions can be p-adically approximated by their Taylor series expansions. Sometimes there is cancellation of the lower order terms, leading to stronger congruences. Using this technique we prove, among other things, a conjecture of Kibelbek and a strengthened version of a conjecture of van Hamme. For the purposes of this paper supercongruences are congruences between terminating hypergeometric series and quotients of p-adic Gamma functions that are stronger than those one can expect to prove using commutative formal group laws. We prove a number of such supercongruences by using classical hypergeometric transformation formulae. These formulae, most of which are decades or centuries old, allow us to write the terminating series as the ratio of products of Γ-values. At this point sums have become quotients. Writing these Γ-quotients as Γ p -quotients, we are in a situation that is well-suited for proving p-adic congruences. These Γ p -functions can be p-adically approximated by their Taylor series expansions. Sometimes there is cancellation of the lower order terms, leading to stronger congruences. Using this technique we prove, among other things, a conjecture of Kibelbek and a strengthened version of a conjecture of van Hamme. Hypergeometric series Elsevier Supercongruences Elsevier p-adic Gamma functions Elsevier Ramakrishna, Ravi oth Enthalten in Elsevier MacKenzie, Shannon M. ELSEVIER Evidence of Titan’s climate history from evaporite distribution 2014 Amsterdam [u.a.] (DE-627)ELV012586625 volume:290 year:2016 day:26 month:02 pages:773-808 extent:36 https://doi.org/10.1016/j.aim.2015.11.043 Volltext GBV_USEFLAG_U GBV_ELV SYSFLAG_U FID-BIODIV SSG-OLC-PHA GBV_ILN_22 GBV_ILN_359 44.94 Hals-Nasen-Ohrenheilkunde VZ AR 290 2016 26 0226 773-808 36 045F 510 |
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10.1016/j.aim.2015.11.043 doi GBVA2016020000011.pica (DE-627)ELV035552050 (ELSEVIER)S0001-8708(15)00521-6 DE-627 ger DE-627 rakwb eng 510 510 DE-600 520 VZ 530 VZ 570 VZ BIODIV DE-30 fid 44.94 bkl Long, Ling verfasserin aut Some supercongruences occurring in truncated hypergeometric series 2016transfer abstract 36 nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier For the purposes of this paper supercongruences are congruences between terminating hypergeometric series and quotients of p-adic Gamma functions that are stronger than those one can expect to prove using commutative formal group laws. We prove a number of such supercongruences by using classical hypergeometric transformation formulae. These formulae, most of which are decades or centuries old, allow us to write the terminating series as the ratio of products of Γ-values. At this point sums have become quotients. Writing these Γ-quotients as Γ p -quotients, we are in a situation that is well-suited for proving p-adic congruences. These Γ p -functions can be p-adically approximated by their Taylor series expansions. Sometimes there is cancellation of the lower order terms, leading to stronger congruences. Using this technique we prove, among other things, a conjecture of Kibelbek and a strengthened version of a conjecture of van Hamme. For the purposes of this paper supercongruences are congruences between terminating hypergeometric series and quotients of p-adic Gamma functions that are stronger than those one can expect to prove using commutative formal group laws. We prove a number of such supercongruences by using classical hypergeometric transformation formulae. These formulae, most of which are decades or centuries old, allow us to write the terminating series as the ratio of products of Γ-values. At this point sums have become quotients. Writing these Γ-quotients as Γ p -quotients, we are in a situation that is well-suited for proving p-adic congruences. These Γ p -functions can be p-adically approximated by their Taylor series expansions. Sometimes there is cancellation of the lower order terms, leading to stronger congruences. Using this technique we prove, among other things, a conjecture of Kibelbek and a strengthened version of a conjecture of van Hamme. Hypergeometric series Elsevier Supercongruences Elsevier p-adic Gamma functions Elsevier Ramakrishna, Ravi oth Enthalten in Elsevier MacKenzie, Shannon M. ELSEVIER Evidence of Titan’s climate history from evaporite distribution 2014 Amsterdam [u.a.] (DE-627)ELV012586625 volume:290 year:2016 day:26 month:02 pages:773-808 extent:36 https://doi.org/10.1016/j.aim.2015.11.043 Volltext GBV_USEFLAG_U GBV_ELV SYSFLAG_U FID-BIODIV SSG-OLC-PHA GBV_ILN_22 GBV_ILN_359 44.94 Hals-Nasen-Ohrenheilkunde VZ AR 290 2016 26 0226 773-808 36 045F 510 |
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10.1016/j.aim.2015.11.043 doi GBVA2016020000011.pica (DE-627)ELV035552050 (ELSEVIER)S0001-8708(15)00521-6 DE-627 ger DE-627 rakwb eng 510 510 DE-600 520 VZ 530 VZ 570 VZ BIODIV DE-30 fid 44.94 bkl Long, Ling verfasserin aut Some supercongruences occurring in truncated hypergeometric series 2016transfer abstract 36 nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier For the purposes of this paper supercongruences are congruences between terminating hypergeometric series and quotients of p-adic Gamma functions that are stronger than those one can expect to prove using commutative formal group laws. We prove a number of such supercongruences by using classical hypergeometric transformation formulae. These formulae, most of which are decades or centuries old, allow us to write the terminating series as the ratio of products of Γ-values. At this point sums have become quotients. Writing these Γ-quotients as Γ p -quotients, we are in a situation that is well-suited for proving p-adic congruences. These Γ p -functions can be p-adically approximated by their Taylor series expansions. Sometimes there is cancellation of the lower order terms, leading to stronger congruences. Using this technique we prove, among other things, a conjecture of Kibelbek and a strengthened version of a conjecture of van Hamme. For the purposes of this paper supercongruences are congruences between terminating hypergeometric series and quotients of p-adic Gamma functions that are stronger than those one can expect to prove using commutative formal group laws. We prove a number of such supercongruences by using classical hypergeometric transformation formulae. These formulae, most of which are decades or centuries old, allow us to write the terminating series as the ratio of products of Γ-values. At this point sums have become quotients. Writing these Γ-quotients as Γ p -quotients, we are in a situation that is well-suited for proving p-adic congruences. These Γ p -functions can be p-adically approximated by their Taylor series expansions. Sometimes there is cancellation of the lower order terms, leading to stronger congruences. Using this technique we prove, among other things, a conjecture of Kibelbek and a strengthened version of a conjecture of van Hamme. Hypergeometric series Elsevier Supercongruences Elsevier p-adic Gamma functions Elsevier Ramakrishna, Ravi oth Enthalten in Elsevier MacKenzie, Shannon M. ELSEVIER Evidence of Titan’s climate history from evaporite distribution 2014 Amsterdam [u.a.] (DE-627)ELV012586625 volume:290 year:2016 day:26 month:02 pages:773-808 extent:36 https://doi.org/10.1016/j.aim.2015.11.043 Volltext GBV_USEFLAG_U GBV_ELV SYSFLAG_U FID-BIODIV SSG-OLC-PHA GBV_ILN_22 GBV_ILN_359 44.94 Hals-Nasen-Ohrenheilkunde VZ AR 290 2016 26 0226 773-808 36 045F 510 |
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10.1016/j.aim.2015.11.043 doi GBVA2016020000011.pica (DE-627)ELV035552050 (ELSEVIER)S0001-8708(15)00521-6 DE-627 ger DE-627 rakwb eng 510 510 DE-600 520 VZ 530 VZ 570 VZ BIODIV DE-30 fid 44.94 bkl Long, Ling verfasserin aut Some supercongruences occurring in truncated hypergeometric series 2016transfer abstract 36 nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier For the purposes of this paper supercongruences are congruences between terminating hypergeometric series and quotients of p-adic Gamma functions that are stronger than those one can expect to prove using commutative formal group laws. We prove a number of such supercongruences by using classical hypergeometric transformation formulae. These formulae, most of which are decades or centuries old, allow us to write the terminating series as the ratio of products of Γ-values. At this point sums have become quotients. Writing these Γ-quotients as Γ p -quotients, we are in a situation that is well-suited for proving p-adic congruences. These Γ p -functions can be p-adically approximated by their Taylor series expansions. Sometimes there is cancellation of the lower order terms, leading to stronger congruences. Using this technique we prove, among other things, a conjecture of Kibelbek and a strengthened version of a conjecture of van Hamme. For the purposes of this paper supercongruences are congruences between terminating hypergeometric series and quotients of p-adic Gamma functions that are stronger than those one can expect to prove using commutative formal group laws. We prove a number of such supercongruences by using classical hypergeometric transformation formulae. These formulae, most of which are decades or centuries old, allow us to write the terminating series as the ratio of products of Γ-values. At this point sums have become quotients. Writing these Γ-quotients as Γ p -quotients, we are in a situation that is well-suited for proving p-adic congruences. These Γ p -functions can be p-adically approximated by their Taylor series expansions. Sometimes there is cancellation of the lower order terms, leading to stronger congruences. Using this technique we prove, among other things, a conjecture of Kibelbek and a strengthened version of a conjecture of van Hamme. Hypergeometric series Elsevier Supercongruences Elsevier p-adic Gamma functions Elsevier Ramakrishna, Ravi oth Enthalten in Elsevier MacKenzie, Shannon M. ELSEVIER Evidence of Titan’s climate history from evaporite distribution 2014 Amsterdam [u.a.] (DE-627)ELV012586625 volume:290 year:2016 day:26 month:02 pages:773-808 extent:36 https://doi.org/10.1016/j.aim.2015.11.043 Volltext GBV_USEFLAG_U GBV_ELV SYSFLAG_U FID-BIODIV SSG-OLC-PHA GBV_ILN_22 GBV_ILN_359 44.94 Hals-Nasen-Ohrenheilkunde VZ AR 290 2016 26 0226 773-808 36 045F 510 |
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Evidence of Titan’s climate history from evaporite distribution |
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Evidence of Titan’s climate history from evaporite distribution |
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some supercongruences occurring in truncated hypergeometric series |
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Some supercongruences occurring in truncated hypergeometric series |
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For the purposes of this paper supercongruences are congruences between terminating hypergeometric series and quotients of p-adic Gamma functions that are stronger than those one can expect to prove using commutative formal group laws. We prove a number of such supercongruences by using classical hypergeometric transformation formulae. These formulae, most of which are decades or centuries old, allow us to write the terminating series as the ratio of products of Γ-values. At this point sums have become quotients. Writing these Γ-quotients as Γ p -quotients, we are in a situation that is well-suited for proving p-adic congruences. These Γ p -functions can be p-adically approximated by their Taylor series expansions. Sometimes there is cancellation of the lower order terms, leading to stronger congruences. Using this technique we prove, among other things, a conjecture of Kibelbek and a strengthened version of a conjecture of van Hamme. |
abstractGer |
For the purposes of this paper supercongruences are congruences between terminating hypergeometric series and quotients of p-adic Gamma functions that are stronger than those one can expect to prove using commutative formal group laws. We prove a number of such supercongruences by using classical hypergeometric transformation formulae. These formulae, most of which are decades or centuries old, allow us to write the terminating series as the ratio of products of Γ-values. At this point sums have become quotients. Writing these Γ-quotients as Γ p -quotients, we are in a situation that is well-suited for proving p-adic congruences. These Γ p -functions can be p-adically approximated by their Taylor series expansions. Sometimes there is cancellation of the lower order terms, leading to stronger congruences. Using this technique we prove, among other things, a conjecture of Kibelbek and a strengthened version of a conjecture of van Hamme. |
abstract_unstemmed |
For the purposes of this paper supercongruences are congruences between terminating hypergeometric series and quotients of p-adic Gamma functions that are stronger than those one can expect to prove using commutative formal group laws. We prove a number of such supercongruences by using classical hypergeometric transformation formulae. These formulae, most of which are decades or centuries old, allow us to write the terminating series as the ratio of products of Γ-values. At this point sums have become quotients. Writing these Γ-quotients as Γ p -quotients, we are in a situation that is well-suited for proving p-adic congruences. These Γ p -functions can be p-adically approximated by their Taylor series expansions. Sometimes there is cancellation of the lower order terms, leading to stronger congruences. Using this technique we prove, among other things, a conjecture of Kibelbek and a strengthened version of a conjecture of van Hamme. |
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Some supercongruences occurring in truncated hypergeometric series |
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