We consider the ratio of two Gauss hypergeometric functions, in which parameters numerator function differ from respective denominator by integers. derive explicit integral representations for this based on a formula its imaginary part. This work extends our recent results lifting certain restrictions parameters. The new are illustrated with few examples and an application to products ratios.

Herein, we build and implement a combination of Lucas polynomials basis that fulfills the spatial homogenous boundary conditions. This is then used to solve time-fractional diffusion equation spectrally. The elements all spectral matrices are explicitly obtained in terms Gauss hypergeometric function. convergence error analysis proposed expansion studied. Numerical results indicate high accurac...

and Dn denotes the derivative operator ∂/∂x1, . . . ,∂xn. The operators in (1.1) provide multidimensional generalizations to the well-known one-dimensional Riemann-Liouville andWeyl fractional integral operators defined in [5] (see also [1]). The paper [7] considers several formulas and interesting properties of (1.1). By invoking the Gauss hypergeometric function 2F1(α,β;γ;x), the following ge...

In a joint paper with Srivastava and Chopra, we introduced far-reaching generalizations of the extended Gammafunction, extended Beta function and the extended Gauss hypergeometric function. In this present paper, we extend the generalized Mittag–Leffler function by means of the extended Beta function. We then systematically investigate several properties of the extended Mittag–Leffler function,...

It is proved that the Laurent expansion of the following Gauss hypergeometric functions, are an arbitrary integer nonnegative numbers, a, b, c are an arbitrary numbers and ε is an arbitrary small parameters, are expressible in terms of the harmonic polylogarithms of Remiddi and Vermaseren with polynomial coefficients. An efficient algorithm for the calculation of the higher-order coefficients o...

Traditionally, the special function theory has many applications in various areas of mathematical physics, economics, statistics, engineering, and other branches science. Inspired by certain recent extensions k-analogue gamma, Pochhammer symbol, hypergeometric functions, this work is devoted to study Gauss functions Hadamard product. We give a definition product k-Gauss (HPkGHF) associated with...

This paper provides a two-fold generalization of the logistic population dynamics to a nonautonomous context. First it is assumed the carrying capacity alone pulses the population behavior changing logistically on its own. In such a way we get again the model of [11], numerically computed by them, and we solve it completely through the Gauss hypergeometric function. Furthermore, both the carryi...

Recently, Hong, Mertens, Ono, and Zhang [8] proved a conjecture of Căldăraru, He, Huang [4] that expresses the Taylor series modular j-function around elliptic points i $$\rho =e^{\pi i/3}$$ as rational functions arising from signature 2 3 cases Ramanujan’s theory to alternative bases. We extend these results give inversion formulas for $$ Gauss’ hypergeometric in signatures 4 6.