A note on generalized q -difference equations for q -beta and Andrews–Askey integral
نویسندگان
چکیده
منابع مشابه
A Note on Generalized q-Boole Polynomials
Let p be a prime number with p ≡ 1(mod 2). Throughout this paper, Zp,Qp and Cp will denote the ring of p-adic integers, the field of p-adic rational numbers and the completion of algebraic closure of Qp. The p-adic norm | · |p is normalized as |p|p = 1 p . Let q be an indeterminate in Cp such that |1− q|p < p −1 p−1 . The q-extension of number x be defined as [x]q = 1−qx 1−q . Note that limq→1[...
متن کاملq-Hypergeometric solutions of q-difference equations
We present algorithm qHyper for finding all solutions y(x) of a linear homogeneous q-difference equation, such that y(qx) = r(x)y(x) where r(x) is a rational function of x. Applications include construction of basic hypergeometric series solutions, and definite q-hypergeometric summation in closed form. ∗The research described in this publication was made possible in part by Grant J12100 from t...
متن کاملAnalytic q-difference equations
A complex number q with 0 < |q| < 1 is fixed. By an analytic q-difference equation we mean an equation which can be represented by a matrix equation Y (z) = A(z)Y (qz) where A(z) is an invertible n× n-matrix with coefficients in the field K = C({z}) of the convergent Laurent series and where Y (z) is a vector of size n. The aim of this paper is to give an overview of our present knowledge of th...
متن کاملSequential Derivatives of Nonlinear q-Difference Equations with Three-Point q-Integral Boundary Conditions
This paper studies sufficient conditions for the existence of solutions to the problem of sequential derivatives of nonlinear qdifference equations with three-point q-integral boundary conditions. Our results are concerned with several quantum numbers of derivatives and integrals. By using Banach’s contraction mapping, Krasnoselskii’s fixed-point theorem, and Leray-Schauder degree theory, some ...
متن کاملOn classical irregular q-difference equations
The primary aim of this paper is to (provide tools in order to) compute Galois groups of classical irregular q-difference equations. We are particularly interested in quantizations of omnipresent differential equations in the mathematical and physical literature, namely confluent generalized q-hypergeometric equations and q-Kloosterman equations.
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: Journal of Mathematical Analysis and Applications
سال: 2014
ISSN: 0022-247X
DOI: 10.1016/j.jmaa.2013.11.027