Results 71 to 80 of about 5,448,308 (166)

A τ‐Deformation of the Basic Horn Function H3 in q‐Calculus

Journal of Function Spaces, Volume 2026, Issue 1, 2026.
Motivated by the growing literature on basic (or q‐) Horn‐type series in quantum calculus and by τ‐extensions of hypergeometric functions, we introduce a generalized basic τ‐confluent Horn hypergeometric function H3. The parameter τ > 0 deforms the unit shift in the q‐gamma factors and thereby interpolates between the standard basic Horn function and a
Maryam G. Alshehri, Oğuz Yağcı, Nada Mostafa, Ayman Shehata, Kwok-Pun Ho   +4 more
wiley   +1 more source

Expansions of the Solutions of the General Heun Equation Governed by Two-Term Recurrence Relations for Coefficients

Advances in High Energy Physics, 2018
We examine the expansions of the solutions of the general Heun equation in terms of the Gauss hypergeometric functions. We present several expansions using functions, the forms of which differ from those applied before.
T. A. Ishkhanyan, T. A. Shahverdyan, A. M. Ishkhanyan   +2 more
doaj   +1 more source

On a problem for mixed type equation with partial riemann-liouville fractional derivative

Vestnik Samarskogo Gosudarstvennogo Tehničeskogo Universiteta. Seriâ: Fiziko-Matematičeskie Nauki, 2016
The uniqueness and existence of solutions of a nonlocal problem proved for an equation of mixed type. This equation contains diffusion equation of fractional order.
Oleg A Repin, Anna V Tarasenko
doaj   +1 more source

Series Solution to a Fuchsian‐Type Differential Equation in Terms of Orthogonal Polynomials

Journal of Mathematics, Volume 2026, Issue 1, 2026.
In this paper, we study a thirteen‐parameter Fuchsian‐type second‐order linear differential equation that involves five regular singularities. By employing a tridiagonal representation technique, we formulate four cases under which the series solutions of the equation are obtained in terms of Jacobi polynomials.
Saiful Rahman Mondal, Pratap Narayan Pathak, Smritijit Sen   +2 more
wiley   +1 more source

HB ?1,?2,?3 Srivastava Hypergeometric Function

, 2019
Formulas and identities involving many well known special functions (such as the Gamma and Betafunctions, Gauss hypergeometric function, and so on) play important roles in themselves and their diverseapplications.
Yağcı, Oğuz
core  

Gauss Hypergeometric Representations of the Ferrers Function of the Second Kind

, 2021
We derive all eighteen Gauss hypergeometric representations for the Ferrers function of the second kind, each with a different argument. They are obtained from the eighteen hypergeometric representations of the associated Legendre function of the second ...
Cohl, Howard S., Volkmer, Hans, Park, Justin   +2 more
core   +1 more source

Certain Results on Extended Beta and Related Functions Using Matrix Arguments

Journal of New Theory
In this study, we present and explore extended beta matrix functions (EBMFs) and their key properties. By utilizing the beta matrix function (BMF), we introduce novel extensions of the Gauss hypergeometric matrix function (GHMF) and Kummer hypergeometric
Saddam Husain, Rakibul Sk, Nabiullah Khan   +2 more
doaj   +1 more source

A Class of Extended Fractional Derivative Operators and Associated Generating Relations Involving Hypergeometric Functions

Axioms, 2012
Recently, an extended operator of fractional derivative related to a generalized Beta function was used in order to obtain some generating relations involving the extended hypergeometric functions [1].
H. M. Srivastava, Rakesh K. Parmar, Purnima Chopra   +2 more
doaj   +1 more source

Solution of abel‐type hypergeometric integral equation

Mathematical Modelling and Analysis, 1997
The paper is devoted to the study of the one‐dimensional integral equation involving the Gauss hypergeometric function in the kernel. The necessary and sufficient conditions for the solvability of such an equation in the space of summable functions are ...
A. A. Kilbas, R. K. Raina, M. Saigo, H. M. Srivastava   +3 more
doaj   +1 more source

H ?1,?2,?3 A Srivastava Hypergeometric Function

, 2018
Formulas and identities involving many well known special functions (such as the Gamma and Betafunctions, Gauss hypergeometric function, and so on) play important roles in themselves and their diverseapplications.
Yağcı, Oğuz, Şahin, Recep
core