A New Class of Functions Suggested by the Generalized Basic Hypergeometric Function

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Authors

  • Meera H. Chudasama
     Department of Mathematics, Faculty of Science, The Maharaja Sayajirao University of Baroda,Vadodara-390 002 ,IN
  • B. I. Dave
     Department of Mathematics, Faculty of Science, The Maharaja Sayajirao University of Baroda, Vadodara-390 002 ,IN

DOI:

https://doi.org/10.18311/jims/2017/14969

Keywords:

Basic Hypergeometric Function, q-derivative, q-integral, Eigen Function, Infinite Order Difference Equation

Abstract

We introduce an extended generalized basic hypergeometric function rΦs+p in which p tends to infinity together with the summation index. We define the difference operators and obtain infinite order difference equation, for which these new special functions are eigen functions. We derive some properties, as the order zero of this function, differential equation involving a particular hyper-Bessel type operators of infinite order, and contiguous function relations. A transformation formula and an l-analogue of the q-Maclaurin's series are also obtained.

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Published

2017-07-01

How to Cite

Chudasama, M. H., & Dave, B. I. (2017). A New Class of Functions Suggested by the Generalized Basic Hypergeometric Function. The Journal of the Indian Mathematical Society, 84(3-4), 161–181. https://doi.org/10.18311/jims/2017/14969

Issue

Volume 84, Issue 3-4, July-December 2017

Section

Articles

License

Copyright (c) 2017 Meera H. Chudasama, B. I. Dave

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

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Europe PMC
Received 2017-02-03
Accepted 2017-04-04
Published 2017-07-01

 

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