q-fractional differentiation and basic hypergeometric transformations
نویسندگان
چکیده
منابع مشابه
Nonterminating Basic Hypergeometric Series and the q-Zeilberger Algorithm
We present a systematic method for proving nonterminating basic hypergeometric identities. Assume that k is the summation index. By setting a parameter x to xqn, we may find a recurrence relation of the summation by using the q-Zeilberger algorithm. This method applies to almost all nonterminating basic hypergeometric summation formulas in the book of Gasper and Rahman. Furthermore, by comparin...
متن کاملInvariance Groups of Three Term Transformations for Basic Hypergeometric Series
The study of invariance groups associated with two term transformations between (basic) hypergeometric series has received its fair share of attention, and indeed, for most two term transformations between (basic) hypergeometric series, the underlying invariance group is explicitly known. In this article, we study the group structure underlying some three term transformation formulae, thereby g...
متن کاملNoncommutative Hypergeometric and Basic Hypergeometric Equations
Recently, J. A. Tirao [Proc. Nat. Acad. Sci. 100 (14) (2003), 8138–8141] considered a matrix-valued analogue of the 2F1 Gauß hypergeometric function and showed that it is the unique solution of a matrix-valued hypergeometric equation analytic at z = 0 with value I, the identity matrix, at z = 0. We give an independent proof of Tirao’s result, extended to the more general setting of hypergeometr...
متن کاملGeneralized basic hypergeometric equations
This paper deals with regular singular generalized q-hypergeometric equations with either “large” or “small” Galois groups. In particular, we consider the fundamental problem of finding appropriate Galoisian substitutes for the usual notion of local monodromy.
متن کاملSummations and Transformations for Multiple Basic and Elliptic Hypergeometric Series by Determinant Evaluations
Abstract. Using multiple q-integrals and a determinant evaluation, we establish a multivariable extension of Bailey’s nonterminating 10φ9 transformation. From this result, we deduce new multivariable terminating 10φ9 transformations, 8φ7 summations and other identities. We also use similar methods to derive new multivariable 1ψ1 and 6ψ6 summations. Some of our results are extended to the case o...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Annales Polonici Mathematici
سال: 1971
ISSN: 0066-2216,1730-6272
DOI: 10.4064/ap-25-2-109-124