On Two General Integrals Involving Humbert's and Kummer's Hypergeometric Functions Ahmed Ali Atash, Hussein Saleh Bellehaj

# On Two General Integrals Involving Humbert's and Kummer's Hypergeometric FunctionsAhmed Ali Atash, Hussein Saleh Bellehaj

Abstract: The aim of this paper is to apply generalized Kummer's theorem and generalized Dixon's theorem due to Lavoie et al. to establish two general integrals involving Humbert's functions of two variables $\varPhi_2$, $\varPsi_2$ and Kummer's function ${}_1F_1$. Some interesting applications of our main results are also presented.

Keywords: Humbert's functions, Kummer's function, Kamp\'{e} de F\'{e}riet function, Generalized Kummer's theorem, Generalized Dixon's theorem.

Ahmed Ali Atash, Hussein Saleh Bellehaj, On Two General Integrals Involving Humbert's and Kummer's Hypergeometric Functions,  International Journal of Advances in Mathematics, Volume 2018, Number 2, Pages 1-8, 2018.