Some classes of generating functions associated with a certain family of extended and generalized hypergeometric functions

A family of the incomplete hypergeometric functions and associated integral transform and fractional derivative formulas

“…The function Γ(z), and its incomplete versions γ(s, x) and Γ(s, x), are known to play important rôles in the study of the analytic solutions of a variety of problems in diverse areas of science and engineering (see, for example, [1], [5], [18] and [29]; see also the recent papers [10], [23], [24], [26], [27], [16], [17], [34], [36], [37] and [38]).…”

Integral transform and fractional derivative formulas involving the extended generalized hypergeometric functions and probability distributions

“…The currently popular literature on Special Functions contains several generalizations of the Gamma function .z/, the Beta function B.˛,ˇ/, the hypergeometric functions 1 F 1 and 2 F 1 , and the generalized hypergeometric functions r F s with r numerator and s denominator parameters (see, for details, [1,2,[8][9][10][11][12][13][14][15][16][17][18][19][20][21] and the references cited in each of these papers). In particular, for an appropriately bounded sequence fÄ`g`2 N0 of essentially arbitrary (real or complex) numbers, Srivastava et al [16, p. 243, Eq.…”

Generalized Srivastava's triple hypergeometric functions and their associated properties

“…and two of the confluent forms of Appell series in two variables defined by For various other investigations involving generalizations of the hypergeometric function r F s of r numerator and s denominator parameters, which were motivated essentially by the work of Srivastava et al [23], the interested reader may be referred to several recent papers on the subject (see, e.g., [10,[21][22][23][24] and the references cited therein).…”