Elliott's identity and hypergeometric functions (original) (raw)
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Using generalized hypergeometric functions to perform symbolic manipulation of equations is of great importance to pure and applied scientists. There are in the literature a great number of identities for the Meijer-G function. On the other hand, when more complex expressions arise, the latter function is not capable of representing them. The H-function is an alternative to overcome this issue, as it is a generalization of the Meijer-G function. In the present paper, a new identity for the H-function is derived. In short, this result enables one to split a particular H-function into the sum of two other H-functions. The new relation in addition to an old result are applied to the summation of hypergeometric series. Finally, some relations between H-functions and elementary functions are built.
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Applied Mathematics and Computation, 2003
Recently, Virchenko et al. [Integral Transform. and Spec. Funct. 12 (1) (2001) 89-100] have defined and studied a generalized hypergeometric function of the form 2 R s 1 ða; b; c; s; zÞ ¼ CðcÞ CðbÞCðc À bÞ Z 1 0 t bÀ1 ð1 À tÞ cÀbÀ1 ð1 À zt s Þ dt: