Fourier transform and distributional representation of the gamma function leading to some new identities (Q1777670)

Summary: We present a Fourier transform representation of the gamma functions, which leads naturally to a distributional representation for them. Both of these representations lead to new identities for the integrals of gamma functions multiplied by other functions, which are also presented here. Editor's remark: Definitions of (incomplete) gamma functions as distributions were given by \textit{Brian Fisher} and co-workers [see, e.g., Rostocker Math. Kolloq. 31, 4--10 (1987; Zbl 0627.33001); J. Math., Punjab Univ. 31, 1--12 (1998; Zbl 0965.46030)]. The present paper does not cite these works.