Certain generalized appell type functions and their properties

Appell considered the product of two Gauss's hypergeometric functions ₂F₁ to devise four Appell's functions F₁, F₂, F₃ and F₄ in two variables. Burchnall and Chaundy, and several others, systematically, presented a number of expansion and decomposition formulas for some double hypergeometric functions, for example, the Appell's functions F_i, in series of simpler hypergeometric functions. Recently, Khan and Abukhammash introduced and investigated 10 Appell type generalized functions M_i (i = 1,.. 10) by considering the product of two ₃F₂ functions. Here, motivated essentially by the above-mentioned works, we aim to introduce 18 Appell type generalized functions κ_i (i = 1,.., 18) by considering the product of two ₄F₃ functions and, among other things, investigate their integral representations. We also present some decomposition formulas of κ_i (i = 1,.., 1 8) and certain relationships among the κ_i (i = 1,.., 1 8) by using symbolic operators.