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The incomplete Lauricella and fourth Appell functions. (English) Zbl 1315.33015
Summary: Recently, H. M. Srivastava et al. [Integral Transforms Spec. Funct. 23, No. 9, 659–683 (2012; Zbl 1254.33004)] introduced the incomplete Pochhammer symbol and studied some fundamental properties and characteristics of a family of potentially useful incomplete hypergeometric functions. Here we introduce the incomplete Lauricella function \(\gamma^{(n)}_C\) and \(\Gamma^{(n)}_C\) of \(n\) variables, and investigate certain properties of the incomplete Lauricella functions, for example, their various integral representations, differential formula and recurrence relation, in a rather systematic manner. Some interesting special cases of our main results are also considered.

33C65 Appell, Horn and Lauricella functions
33B15 Gamma, beta and polygamma functions
33B20 Incomplete beta and gamma functions (error functions, probability integral, Fresnel integrals)
33C05 Classical hypergeometric functions, \({}_2F_1\)
33C15 Confluent hypergeometric functions, Whittaker functions, \({}_1F_1\)
33C20 Generalized hypergeometric series, \({}_pF_q\)
DLMF; Equator
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