On generalization of Bailey's identity involving product of generalized hypergeometric series

• Published in: arXiv.org 2017-02
• Main Authors: Kim, Y S, Rathie, A K
• Format: Article
• Language: English
• Subjects: Arrays; Scientific papers
• ISSN: 2331-8422

The aim of this research paper is to obtain explicit expressions of (i) \( {}_1F_1 \left[\begin{array}{c} \alpha \\ 2\alpha + i \end{array} ; x \right]. {}_1F_1\left[ \begin{array}{c} \beta \\ 2\beta + j \end{array} ; x \right]\) (ii) \({}_1F_1 \left[ \begin{array}{c} \alpha \\ 2\alpha - i \end{array} ; x \right] . {}_1F_1 \left[ \begin{array}{c} \beta \\ 2\beta - j \end{array} ; x \right]\) (iii) \({}_1F_1 \left[ \begin{array}{c} \alpha \\ 2\alpha + i \end{array} ; x \right] . {}_1F_1 \left[\begin{array}{c} \beta \\ 2\beta - j \end{array} ; x \right]\) in the most general form for any \(i,j=0,1,2,\ldots\) For \(i=j=0\), we recover well known and useful identity due to Bailey. The results are derived with the help of a well known Bailey's formula involving products of generalized hypergeometric series and generalization of Kummer's second transformation formulas available in the literature. A few interesting new as well as known special cases have also been given.