Hypergeometric functions are divided into complete and confluent functions. For the first time, Srivastava and Karlsson described a method for constructing a set of all possible triple Gaussian hypergeometric series and compiled a table showing definitions and areas of convergence for 205 different complete series (Srivastava-Karlsson List) depending on three variables. Several authors subsequently obtained various integral representations and transformations for the functions proposed by Srivastava and Karlsson. In this work we compile integral representations and transformation formulas for all confluent forms of one complete hypergeometric function in three variables from the Srivastava-Karlsson List.To prove integral representations for 8 confluent hypergeometric functions of three variables, properties of beta and gamma functions are used. The Boltz formula allows us to derive transformation formulas for the confluent functions under consideration.
| Mualliflar | Ergashev , Tuhtasin, Hasanov , Anvardjan, Safarbayeva , Nigora |
|---|---|
| Jurnal | O‘zbekiston matematika jurnali |
| Nashr sanasi | 2025-11-03 |
| Jild | 69 |
| Son | 4 |
| Betlar | 96-107 |
| Til | Ingliz |
| DOI | 10.29229/uzmj.2025-4-10 |
DOI: 10.29229/uzmj.2025-4-10 · Maqolaning asl sahifasi
Euler type integral representation, transformation formula, confluent hypergeometric functions in three variables, beta function, gamma function
In the paper, we consider a class dynamic control system with a discrete parameter and under conditions of uncertainty in the initial data. The optimal control problem of the minimax type is formulated for a non-smooth…
In this paper we study a ratio-dependent predator-prey model with a free boundary caused by predator-prey interaction over a one dimensional habitat. We study the long time behaviors of the two species and prove a…
We analyze an evasion differential game involving one evader and multiple pursuers in $\R^n$. The control functions of the players are subject to exponential integral constraints to ensure bounded energy consumption…
Let $B$ be a complete Boolean algebra, let $Q(B)$ be the Stone compact of $B$, let $C_\infty (Q(B))$ be the commutative unital algebra of all continuous functions $x:Q(B) \rightarrow [-\infty,+\infty],$…
This paper studies an analog of the Tricomi problem for a loaded parabolic-hyperbolic equation of the second kind, which degenerates inside the domain. In proving the existence and uniqueness theorem for a classical…
Let $Q$ be the field of rational numbers and $Q^{2}$ be the $2$-dimensional linear space over $Q$. A classification of all non-degenerate symmetric bilinear-metric forms over $Q^{2}$ have obtained. Let $\varphi $ be a…
In this paper the spectral properties of the nonlocal Samarskii-Ionkin type problems for a fourth-order ordinary differential equation are investigated. The eigenvalues and corresponding eigenfunctions are found and…
Let $R$ be a ring, and let $M$ be a right $R$-module. Recently, Baannon and Khalid introduced and studied the concept of $e^*$-essential submodules, extending the notion of essential submodules. In this context…
In this paper, an initial-boundary value problem with local and nonlocal conditions for a degenerate partial differential equation of high even order in a rectangle is formulated and investigated. The method of energy…
In this paper, we classify the symmetric Leibniz algebras whose underlying Lie algebra is almost filiform. We also describe the symmetric Leibniz algebras associated with Heisenberg and triangular Lie algebras…