"Appell hypergeometric series"의 두 판 사이의 차이

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==메모==
 
* Clingher, Adrian, Charles F. Doran, and Andreas Malmendier. “Special Function Identities from Superelliptic Kummer Varieties.” arXiv:1510.06435 [math], October 21, 2015. http://arxiv.org/abs/1510.06435.
 
* Clingher, Adrian, Charles F. Doran, and Andreas Malmendier. “Special Function Identities from Superelliptic Kummer Varieties.” arXiv:1510.06435 [math], October 21, 2015. http://arxiv.org/abs/1510.06435.
 
* Bringmann, Kathrin, Jan Manschot, and Larry Rolen. “Identities for Generalized Appell Functions and the Blow-up Formula.” arXiv:1510.00630 [math], October 2, 2015. http://arxiv.org/abs/1510.00630.
 
* Bringmann, Kathrin, Jan Manschot, and Larry Rolen. “Identities for Generalized Appell Functions and the Blow-up Formula.” arXiv:1510.00630 [math], October 2, 2015. http://arxiv.org/abs/1510.00630.
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* Matsumoto, Keiji, Takeshi Sasaki, Tomohide Terasoma, and Masaaki Yoshida. ‘An Example of Schwarz Map of Reducible Hypergeometric Equation $E_2$ in Two Variables’. arXiv:1503.07623 [math], 26 March 2015. http://arxiv.org/abs/1503.07623.
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* Matsumoto, Keiji, Takeshi Sasaki, Tomohide Terasoma, and Masaaki Yoshida. ‘An Example of Schwarz Map of Reducible Hypergeometric Equation <math>E_2</math> in Two Variables’. arXiv:1503.07623 [math], 26 March 2015. http://arxiv.org/abs/1503.07623.
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== 노트 ==
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===말뭉치===
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# In this paper we present a finite field analogue for one of the Appell series.<ref name="ref_6c918006">[https://www.sciencedirect.com/science/article/pii/S1071579717300977 An Appell series over finite fields]</ref>
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# Recently, finite field alanogues of Appell series F1, F2 and F3 are introduced and their relations with certain Gaussian hypergeometric series are established.<ref name="ref_4d1fb6be">[http://gyan.iitg.ernet.in/handle/123456789/1795 Appell series over finite fields and Gaussian hypergeometric series]</ref>
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# We then establish finite field analogues of classical identities satisfied by the Appell series and hypergeometric series.<ref name="ref_4d1fb6be" />
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# We use properties of Gauss and Jacobi sums and our works on finite field Appell series to deduce these product formulas satisfied by the Gaussian hypergeometric series.<ref name="ref_4d1fb6be" />
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# In this paper we give a finite field analogue of Appell series and obtain some transformation and reduction formulas.<ref name="ref_15931b7e">[https://ui.adsabs.harvard.edu/abs/arXiv:1701.02674 Some new formulas for Appell series over finite fields]</ref>
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# We also establish the generating functions for Appell series over finite fields.<ref name="ref_15931b7e" />
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# A FINITE FIELD ANALOGUE FOR APPELL SERIES F3 BING HE Abstract.<ref name="ref_0611877e">[https://vixra.org/pdf/1704.0093v1.pdf A finite field analogue for appell series f3]</ref>
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# In this paper we introduce a nite eld analogue for the Appell series F3 and give some reduction formulae and certain generating functions for this function over nite elds.<ref name="ref_0611877e" />
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# Appell series F3 over nite elds, reduction formula, transformation formula, generating function.<ref name="ref_0611877e" />
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# In that paper, the nite eld analogue of the Appell series F1 was given by F1(A; B, B(cid:48); C; x, y) = (xy)AC(1) (cid:88) u A(u)AC(1 u)B(1 ux)B(cid:48)(1 uy).<ref name="ref_0611877e" />
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# The Appell series F2 is a hypergeometric series in two vari- ables that was introduced by Paul Appell in 1880 as generalization of Gauss hy- pergeometric series 2F1 of one variable.<ref name="ref_f3efc1cc">[http://www.cs.umsl.edu/~clingher/superkummer.pdf Asian j. math.]</ref>
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# In 1933 Bailey derived a reduction formula for the Appell series F4 as product of two Gauss hypergeometric functions.<ref name="ref_f3efc1cc" />
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===소스===
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<references />
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== 메타데이터 ==
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===위키데이터===
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* ID :  [https://www.wikidata.org/wiki/Q4780998 Q4780998]
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===Spacy 패턴 목록===
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* [{'LOWER': 'appell'}, {'LOWER': 'series'}]
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* [{'LOWER': 'appell'}, {'LEMMA': 'series'}]
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* [{'LOWER': 'appell'}, {'LOWER': 'hypergeometric'}, {'LEMMA': 'series'}]
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* [{'LOWER': 'appell'}, {'LOWER': 'hypergeometric'}, {'LEMMA': 'function'}]
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2022년 7월 6일 (수) 19:52 기준 최신판

메모

  • Clingher, Adrian, Charles F. Doran, and Andreas Malmendier. “Special Function Identities from Superelliptic Kummer Varieties.” arXiv:1510.06435 [math], October 21, 2015. http://arxiv.org/abs/1510.06435.
  • Bringmann, Kathrin, Jan Manschot, and Larry Rolen. “Identities for Generalized Appell Functions and the Blow-up Formula.” arXiv:1510.00630 [math], October 2, 2015. http://arxiv.org/abs/1510.00630.
  • Matsumoto, Keiji, Takeshi Sasaki, Tomohide Terasoma, and Masaaki Yoshida. ‘An Example of Schwarz Map of Reducible Hypergeometric Equation \(E_2\) in Two Variables’. arXiv:1503.07623 [math], 26 March 2015. http://arxiv.org/abs/1503.07623.


노트

말뭉치

  1. In this paper we present a finite field analogue for one of the Appell series.[1]
  2. Recently, finite field alanogues of Appell series F1, F2 and F3 are introduced and their relations with certain Gaussian hypergeometric series are established.[2]
  3. We then establish finite field analogues of classical identities satisfied by the Appell series and hypergeometric series.[2]
  4. We use properties of Gauss and Jacobi sums and our works on finite field Appell series to deduce these product formulas satisfied by the Gaussian hypergeometric series.[2]
  5. In this paper we give a finite field analogue of Appell series and obtain some transformation and reduction formulas.[3]
  6. We also establish the generating functions for Appell series over finite fields.[3]
  7. A FINITE FIELD ANALOGUE FOR APPELL SERIES F3 BING HE Abstract.[4]
  8. In this paper we introduce a nite eld analogue for the Appell series F3 and give some reduction formulae and certain generating functions for this function over nite elds.[4]
  9. Appell series F3 over nite elds, reduction formula, transformation formula, generating function.[4]
  10. In that paper, the nite eld analogue of the Appell series F1 was given by F1(A; B, B(cid:48); C; x, y) = (xy)AC(1) (cid:88) u A(u)AC(1 u)B(1 ux)B(cid:48)(1 uy).[4]
  11. The Appell series F2 is a hypergeometric series in two vari- ables that was introduced by Paul Appell in 1880 as generalization of Gauss hy- pergeometric series 2F1 of one variable.[5]
  12. In 1933 Bailey derived a reduction formula for the Appell series F4 as product of two Gauss hypergeometric functions.[5]

소스

  1. ↑ An Appell series over finite fields
  2. ↑ 2.0 2.1 2.2 Appell series over finite fields and Gaussian hypergeometric series
  3. ↑ 3.0 3.1 Some new formulas for Appell series over finite fields
  4. ↑ 4.0 4.1 4.2 4.3 A finite field analogue for appell series f3
  5. ↑ 5.0 5.1 Asian j. math.

메타데이터

위키데이터

Spacy 패턴 목록

  • [{'LOWER': 'appell'}, {'LOWER': 'series'}]
  • [{'LOWER': 'appell'}, {'LEMMA': 'series'}]
  • [{'LOWER': 'appell'}, {'LOWER': 'hypergeometric'}, {'LEMMA': 'series'}]
  • [{'LOWER': 'appell'}, {'LOWER': 'hypergeometric'}, {'LEMMA': 'function'}]
원본 주소 "https://wiki.mathnt.net/index.php?title=Appell_hypergeometric_series&oldid=53034"