Summary: An application of various types of multiple hypergeometric functions in the study of noise immunity of reception of signal constructions in the communication theory are demonstrated. A mathematical model of the communication channel with general fading of the form \(y\left(t\right)=\alpha s_r\left(t\right)+n\left(t\right)\) is considered, where \(s_r\left(t\right)\) is the transmitter signal, \(n\left(t\right)\) is the additive white Gauss noise, and \(\alpha\) is the transmission coefficient, which in the communication channel with fading is a random variable described by a distribution function. The Rice-Nakagami and four-parameter distributions are considered which include a three-parameter distribution (the Beckmann distribution); a two-parameter Hoyt distribution (Nakagami-\(q\)); Rice distribution (Nakagami-\(n\)); Rayleigh distribution; one-sided normal distribution with zero variance and zero expectation. For the representation of moments of distributions, a new general special integral function \(\mathcal{S}_{p,q}\left(w,z;b_1,b_2;\eta\right)\) is introduced which generalizes the \(\mathcal{H} \)-function due to N. V. Savischenko and the Owen function. Various properties including formulas of reduction, differentiation and integration are obtained. The Mellin transforms of some expressions involving the \(\mathcal{H} \)-function are derived. The second type of representations is based on the function \(H_A^{(c)}\left(a_1,a_2;c_1,c_2;x,y,z\right)\), which is a confluent case of the multiple hypergeometric function \(H_A\left(a_1,a_2,a_3;c_1,c_2;x,y,z\right)\) defined as a hypergeometric series of three variables by H. M. Srivastava. For this function, formulas of confluence, reduction, differentiation, as well as integral and series representations are derived.