相关论文: Applications of the operator $H(\alpha,\beta)$ to …
By making use of some techniques based upon certain inverse new pairs of symbolic operators, the author investigate several decomposition formulas associated with Lauricella's hypergeometric functions $F_A^{(r)}, F_B^{(r)}, F_C^{(r)}$ and…
With the help of some techniques based on certain inverse pairs of symbolic operators, the authors investigated several decomposition formulas associated with Srivastava's Hypergeometric functions of three variables. Some operator…
The main object of this work is to show how some rather elementary techniques based upon certain inverse pairs of symbolic operators would lead us easily to several decomposition formulas associated with confluent hypergeometric functions…
The main aim of the present work is to give some interesting the $q$-analogues of various $q$-recurrence relations, $q$-recursion formulas, $q$-partial derivative relations, $q$-integral representations, transformation and summation…
The leading asymptotic behaviour of the Humbert functions $\Phi_2$, $\Phi_3$, $\Xi_2$ of two variables is found, when the absolute values of the two independent variables become simultaneosly large. New integral representations of these…
Humbert confluent hypergeometric functions of two variables arise in many problems of mathematical physics and applied analysis, yet their behavior with respect to parameters has not been systematically studied. In this paper we investigate…
The main aim of this work is to derive the $q$-recurrence relations, $q$-partial derivative relations and summation formula of bibasic Humbert hypergeometric function $\Phi_1$ on two independent bases $q$ and $q_{1}$ of two variables and…
This paper systematically studies the asymptotics of Humbert's bivariate confluent hypergeometric function $\Phi_1[a,b;c;x, y]$. Specifically, we establish explicit asymptotic expansions in five distinct regimes: (i) $x\to\infty$; (ii)…
The study is devoted to the construction of dynamical symmetry algebra of confluent hypergeometric function $_1F_1$ and $\Psi_2$-Humbert function and to derive some generating relations and reduction formulas for $_1F_1$ and $\Psi_2$…
We significantly advance the research program initiated in "Moment-Based Evidence for Simple Rational-Valued Hilbert-Schmidt Generic 2 x 2 Separability Probabilities" (J. Phys. A, 45, 095305 [2012]). A function P(alpha), incorporating a…
We report major advances in the research program initiated in "Moment-Based Evidence for Simple Rational-Valued Hilbert-Schmidt Generic 2 x 2 Separability Probabilities" (J. Phys. A, 45, 095305 [2012]). A highly succinct separability…
Given the growing quantity of proposals and works of basic hypergeometric functions in the scope of $q$-calculus, it is important to introduce a systematic classification of $q$-calculus. Our aim in this article is to investigate certain…
The theoretical computing of special values assumed by the hypergeometric functions has a high interest not only on its own, but also in sight of the remarkable implications to both pure Mathematics and Mathematical Physics. Accordingly, in…
We consider the decomposition of bounded linear operators on Hilbert spaces in terms of functions forming frames. Similar to the singular-value decomposition, the resulting frame decompositions encode information on the structure and…
Using the bicomplex numbers $\mathbb{T}$ which is a commutative ring with zero divisors defined by $\mathbb{T}=\{w_0 + w_1 i_1 + w_2 i_2 + w_3 j | w_0, w_1, w_2, w_3 \in \mathbb{R}\}$ where $i_{1}^{2} = -1, i_{2}^{2} = -1, j^2 = 1, i_1 i_2…
Highest-weight representations of infinite dimensional Lie algebras and Hilbert schemes of points are considered, together with the applications of these concepts to partition functions, which are most useful in physics. Partition functions…
For finding the numerical solution of operator equations in many applications a decomposition in subspaces is needed. Therefore, it is necessary to extend the known method of matrix representation to the utilization of fusion frames. In…
We derive some Euler type double integral representations for hypergeometric functions in two variables. In the first part of this paper we deal with Horn's $H_2$ function, in the second part with Olsson's $F_P$ function. Our double…
We show that any m-isometric tuples of commuting operators on a finite dimensional Hilbert space can be decomposed as a sum of a spherical isometry and a commuting nilpotent tuple. Our approach applies as well to tuples of algebraic…
We present two algorithms for computing hypergeometric solutions of second order linear differential operators with rational function coefficients. Our first algorithm searches for solutions of the form \[ \exp(\int r \,…