Multiple elliptic hypergeometric series. An approach from the Cauchy determinant

By Yasushi Kajihara, M. Noumi. 2003

85 citations recorded by the source corpus.

Abstract A multiple generalization of elliptic hypergeometric series is studied through the Cauchy determinant for the Weierstrass sigma function. In particular, a duality transformation for multiple hypergeometric series is proposed. As an application, two types of Bailey transformations for very well-poised multiple elliptic hypergeometric series are derived.

Subfields: Algebra and Number Theory, Applied Mathematics, Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/0efb9a507b9583e2685cebf7d5ff3098dbb78d39

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Algebra and Number Theory

1. Eric M. Rains
2. Michael J. Schlosser
3. V. Spiridonov
4. Christian Krattenthaler
5. Hjalmar Rosengren
6. Zhi-Guo Liu
7. Jeremy Lovejoy
8. Alexei Borodin

In Applied Mathematics

1. Christian Krattenthaler
2. Hjalmar Rosengren
3. Eric M. Rains
4. Michael J. Schlosser
5. V. Spiridonov
6. Zhi-Guo Liu
7. Jeremy Lovejoy
8. Tom H. Koornwinder

In Computational Theory and Mathematics

1. Christian Krattenthaler
2. Hjalmar Rosengren
3. Eric M. Rains
4. Michael J. Schlosser
5. V. Spiridonov
6. G. Vartanov

Citations in the corpus

• Elliptic determinant evaluations and the Macdonald identities for affine root systems (2005, methodology): “Indeed, special cases of our identities have found applications to multidimensional basic and elliptic hypergeometric series and integrals, see [GK], [ KN ], [Ra1], [Ra2], [R1], [R2], [RS1], [S1], [S2], [S3], [S4], [Sp], [W], to the study of Ruijsenaars operators and related integrable systems [H], ”
• Transformations of elliptic hypergeometric integrals (2010, background): “It appears that this can be viewed as an integral analogue of a series transformation of Rosengren [27] and Kajihara and Noumi [12], in that the latter should be derivable via residue calculus from the former.”
• Advanced Determinant Calculus: A Complement (2005, methodology): “r example, ADVANCED DETERMINANT CALCULUS: A COMPLEMENT 71 determinant evaluations involving elliptic functions have come into the picture in the theory of multiple elliptic hypergeometric series, see [95, 147, 152, 153, 155, 176, 187]. They have also an important role in the study of Ruijsenaars ope”
• Transformations of elliptic hypergometric integrals (2003, background): “Again, apparently related series identities are known; see [26] and [12].”