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

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The aim of this research paper is to obtain explicit expressions of (i) ₁F₁ [arrayc α 2α+ i array; x]. ₁F₁[arrayc β 2β+ j array; x] (ii) ₁F₁ [arrayc α 2α- i array; x]. ₁F₁ [arrayc β 2β- j array; x] (iii) ₁F₁ [arrayc α 2α+ i array; x]. ₁F₁ [arrayc β 2β- j array; x] in the most general form for any i,j=0,1,2, 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.