ANDREWS’ TYPE WP-BAILEY LEMMA AND ITS APPLICATIONS

By

Yashoverdhan Vyas1 , Shivani Pathak2 and Kalpana Fatawat3,* 

1,2Department of Mathematics, School of Engineering, Sir Padampat Singhania University, Bhatewar, Udaipur-313601, Rajasthan, India 

3Techno India NJR Institute of Technology, Plot SPL-T, Bhamashah (RIICO) Industrial Area, Kaladwas, Udaipur-313003, Rajasthan, India Email:yashoverdhan.vyas@spsu.ac.in, shivani.bhatt@spsu.ac.in,E-Mail: kalpana.fatawat@technonjr.org*

 (Received : May 03, 2022 ; Revised : May 28, 2022 ; Accepted : June 03, 2022) 

  DOI: https://doi.org/10.58250/Jnanabha.2022.52130

Abstract

Over the years, the study of Bailey transform, Bailey lemma, Bailey pair, their variants and their applications are the major subjects of interest. Of course, it is due to the efficiency of the Bailey transform and lemma in producing many ordinary and q-hypergeometric identities, multiple series summation and transformation formulas, and the Rogers-Ramanujan type identities. Andrews investigated a WP-Bailey lemma and the pairs with the help of Bailey transform and used it to derive well-known summations and multiple series transformations. In this research paper, we investigate an Andrews’ type WP-Bailey lemma and the pairs with the help of First Bailey Type Transform due to Joshi and Vyas. The investigated Andrews’ type WP-Bailey lemma is then applied to obtain terminating multiple q-hypergeometric identities and construct the WP-Bailey type chains and a binary tree. 

The paper is motivated by the observation that the basic (or q-) series and basic (or q-) polynomials, especially the basic (or q-) gamma and q-hypergeometric functions and basic (or q-) hypergeometric polynomials, are applicable particularly in several diverse areas including number theory, theory of partitions and combinatorial analysis as well as in the study of combinatorial generating functions. 

2020 Mathematical Sciences Classification: 33D15, 33D90 

Keywords and Phrases: Andrew’s type WP-Bailey lemma, pairs and chains; Bailey transform, lemma and pairs; First Bailey Type Transform; WP-Bailey lemma, pairs and chains; Multiple q-hypergeometric identities