The incomplete Pochhammer symbols and their applications to hypergeometric and related functions
H. M. Srivastava, M. Aslam Chaudhry, Ravi P. Agarwal · Integral Transforms and Special Functions · 2011
By means of the familiar incomplete gamma functions γ(s, x) and Γ(s, x), we introduce the incomplete Pochhammer symbols that lead us to a natural generalization and decomposition of a class of hypergeometric and other related functions which are potentially useful in closed-form representations of definite and semi-infinite integrals of various special functions. Applications of these functions in (for example) communication theory, probability theory and groundwater pumping modelling are shown.