Dedicated to Srinivasa Ramanujan on the occasion of his 125th birth anniversary.
A Note on q-Integrals and Certain Generating Functions†
Version of Record online: 30 JAN 2013
© 2013 by the Massachusetts Institute of Technology
Studies in Applied Mathematics
Volume 131, Issue 2, pages 105–118, August 2013
How to Cite
Cao, J. (2013), A Note on q-Integrals and Certain Generating Functions. Studies in Applied Mathematics, 131: 105–118. doi: 10.1111/sapm.12002
- Issue online: 24 JUL 2013
- Version of Record online: 30 JAN 2013
- Manuscript Received: 11 DEC 2012
- Tianyuan Special Funds of the National Natural Science Foundation of China. Grant Number: 11226298
- China Postdoctoral Science Foundation. Grant Number: 2012M521155
- Zhejiang Projects for Postdoctoral Research Preferred Funds. Grant Number: Bsh1201021
In this paper, generalizations of certain q-integrals are given by the method of q-difference equation, which involves the Andrews–Askey integral. In addition, some mixed generating functions for generalized Rogers–Szegö polynomials are obtained by the technique of q-integral. More over, generating functions for generalized Andrews–Askey polynomials are achieved by q-integral.