On the q-Analogues of Srivastava's Triple Hypergeometric Functions
نویسنده
چکیده
We find Euler integral formulas, summation and reduction formulas for q-analogues of Srivastava’s three triple hypergeometric functions. The proofs use q-analogues of Picard’s integral formula for the first Appell function, a summation formula for the first Appell function based on the Bayley–Daum formula, and a general triple series reduction formula of Karlsson. Many of the formulas are purely formal, since it is difficult to find convergence regions for these functions of several complex variables. We use the Ward q-addition to describe the known convergence regions of q-Appell and q-Lauricella functions.
منابع مشابه
q-HYPERGEOMETRIC PROOFS OF POLYNOMIAL ANALOGUES OF THE TRIPLE PRODUCT IDENTITY, LEBESGUE’S IDENTITY AND EULER’S PENTAGONAL NUMBER THEOREM
X iv :m at h/ 02 03 22 9v 1 [ m at h. C O ] 2 2 M ar 2 00 2 2000]Primary 05A19, 33D15 q-HYPERGEOMETRIC PROOFS OF POLYNOMIAL ANALOGUES OF THE TRIPLE PRODUCT IDENTITY, LEBESGUE’S IDENTITY AND EULER’S PENTAGONAL NUMBER THEOREM S. OLE WARNAAR Abstract. We present alternative, q-hypergeometric proofs of some polynomial analogues of classical q-series identities recently discovered by Alladi and Berk...
متن کاملOn a Hypergeometric Identity of Gelfand, Graev and Retakh
A hypergeometric identity equating a triple sum to a single sum, originally found by Gelfand, Graev and Retakh [Russian Math. Surveys 47 (1992), 1–88] by using systems of differential equations, is given hypergeometric proofs. As a bonus, several q-analogues can be derived.
متن کاملGalois groups of the basic hypergeometric equations 1 by
In this paper we compute the Galois groups of basic hypergeometric equations. In this paper q is a complex number such that 0 < |q| < 1. 1 Basic hypergeometric series and equations The theory of hypergeometric functions and equations dates back at least as far as Gauss. It has long been and is still an integral part of the mathematical literature. In particular, the Galois theory of (generalize...
متن کاملGalois groups of the basic hypergeometric equations 1 by Julien Roques 20 th of August 2007
In this paper we compute the Galois groups of basic hypergeometric equations. In this paper q is a complex number such that 0 < |q| < 1. 1 Basic hypergeometric series and equations The theory of hypergeometric functions and equations dates back at least as far as Gauss. It has long been and is still an integral part of the mathematical literature. In particular, the Galois theory of (generalize...
متن کاملBrownian motion on time scales, basic hypergeometric functions, and some continued fractions of Ramanujan
Abstract: Motivated by Lévy’s characterization of Brownian motion on the line, we propose an analogue of Brownian motion that has as its state space an arbitrary unbounded closed subset of the line: such a process will a martingale, has the identity function as its quadratic variation process, and is “continuous” in the sense that its sample paths don’t skip over points. We show that there is a...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- Axioms
دوره 2 شماره
صفحات -
تاریخ انتشار 2013