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تسجيل مستخدم جديدOn generalization of Baileys identity involving product of generalized hypergeometric series
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The aim of this research paper is to obtain explicit expressions of (i) $ {}_1F_1 left[begin{array}{c} alpha 2alpha + i end{array} ; x right]. {}_1F_1left[ begin{array}{c} beta 2beta + j end{array} ; x right]$ (ii) ${}_1F_1 left[ begin{array}{c} alpha 2alpha - i end{array} ; x right] . {}_1F_1 left[ begin{array}{c} beta 2beta - j end{array} ; x right]$ (iii) ${}_1F_1 left[ begin{array}{c} alpha 2alpha + i end{array} ; x right] . {}_1F_1 left[begin{array}{c} beta 2beta - j end{array} ; x right]$ 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 Baileys formula involving products of generalized hypergeometric series and generalization of Kummers second transformation formulas available in the literature. A few interesting new as well as known special cases have also been given.
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