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Relations between Lauricella's triple hypergeometric function $F_A^{(3)}(x,\,y,\,z)$ and Exton's function $X_{8}$

DOI: 10.1186/1687-1847-2013-34

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Abstract:

Very recently Choi et al. derived some interesting relations between Lauricella's triple hypergeometric function $F_A^{(3)}(x,\,y,\,z)$ and the Srivastava function $F^{(3)}[x,\,y,\,z]$ by simply splitting Lauricella's triple hypergeometric function $F_A^{(3)}(x,\,y,\,z)$ into eight parts. Here, in this paper, we aim at establishing eleven new and interesting transformations between Lauricella's triple hypergeometric function $F_A^{(3)}(x,\,y,\,z)$ and Exton's function $X_{8}$ in the form of a single result. Our results presented here are derived with the help of two general summation formulae for the terminating ${}_2F_1(2)$ series which were very recently obtained by Kim et al. and also include the relationship between $F_A^{(3)}(x,\,y,\,z)$ and $X_{8}$ due to Exton.

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