By means of the spherical functions associated to Gelfand pair \((\mathbb {H}_{n},U(n))\) we define operator \(L+\alpha |T|\), where L denotes Heisenberg sublaplacian and T central element Lie algebra, establish a notion fundamental solution explicitly compute in terms Gauss hypergeometric function. For \(\alpha <n\) use Integral Representation Theorem obtain more detailed expression. Finally, ...

We study a 3–parametric family of stochastic point processes on the one–dimensional lattice originated from a remarkable family of representations of the infinite symmetric group. We prove that the correlation functions of the processes are given by determinantal formulas with a certain kernel. The kernel can be expressed through the Gauss hypergeometric function; we call it the hypergeometric ...

Our main goal in this paper is to investigate stochastic ternary antiderivatives (STAD). First, we will introduce the random antiderivative operator. Then, by introducing aggregation function using special functions such as Mittag-Leffler (MLF), Wright (WF), H-Fox (HFF), Gauss hypergeometric (GHF), and exponential (EXP-F), select optimal control performing necessary calculations. Next, consider...

Three term recurrence relations yn+1+bnyn+anyn−1 = 0 can be used for computing recursively a great number of special functions. Depending on the asymptotic nature of the function to be computed, different recursion directions need to be considered: backward for minimal solutions and forward for dominant solutions. However, some solutions interchange their role for finite values of n with respec...

There are many extensions and generalizations of Gamma Beta functions in the literature. However, a new extension extended function B_(ζ〖, α〗_1)^(α_2;〖 m〗_1,〖 m〗_2 ) (a_1,a_2 was introduced presented here because its important properties. The has symmetric property, integral representations, Mellin transform, inverse transform statistical properties like distribution, mean, variance, moment cum...

By employing two well-known Euler’s transformations for the hypergeometric function 2F1, Liu and Wang established numerous general transformation reduction formulas Kampé de Fériet deduced many new summation with aid of classical theorems 2F1 due to Kummer, Gauss Bailey. Here, by making a fundamental use above-mentioned formulas, we aim establish 32 help generalizations above-referred Relevant ...

Riordan matrix methods and manipulation of various generating functions are used to find curious relations among the Catalan, central binomial, and RNA generating functions. In addition, the Wilf-Zeilberger method is used to find identities where the gamma function and Catalan numbers are expressed in terms of the Gauss hypergeometric function. As a consequence of the identities, new recurrence...

A fourth order fixed point method to compute the zeros of solutions of second order homogeneous linear ODEs is obtained from the approximate integration of the Riccati equation associated with the ODE. The method requires the evaluation of the logarithmic derivative of the function and also uses the coefficients of the ODE. An algorithm to compute with certainty all the zeros in an interval is ...