Related papers: Computations of general Heun functions from their …
We present numerical techniques based on generalized functions adapted to nonlinear calculations. They concern main numerical engineering problems ruled by-or issued from-nonlinear equations of continuum mechanics. The aim of this text is…
In this paper, we introduce a method of converting implicit equations to the usual forms of functions locally without differentiability. For a system of implicit equations which are equipped with continuous functions, if there are unique…
We study the incomplete Mellin transformation of the fractional part and the related log-sine function when composed by an affine complex map. We evaluate the corresponding integral in two different ways which yields equalities with series…
We develop numerical algorithms for the efficient evaluation of quantities associated with generalized matrix functions [J. B. Hawkins and A. Ben-Israel, Linear and Multilinear Algebra 1(2), 1973, pp. 163-171]. Our algorithms are based on…
In the paper, the well-known quantum mechanical problem of a spin 1/2 particle in external Coulomb potential, reduced to a system of two first-order differential equations, is studied from the point of view of possible applications of the…
Starting from equations obeyed by functions involving the first or the second derivatives of the biconfluent Heun function, we construct two expansions of the solutions of the biconfluent Heun equation in terms of incomplete Beta functions.…
We consider the derivatives of Horn hypergeometric functions of any number variables with respect to their parameters. The derivative of the function in $n$ variables is expressed as a Horn hypergeometric series of $n+1$ infinite summations…
We provide a set of diagonals of simple rational functions of three and four variables that are squares of Heun functions. These Heun functions obtained through creative telescoping, turn out to be either pullbacked $_2F_1$ hypergeometric…
We derive a concise closed-form solution for a linear three-term recurrence relation. Such recurrence relations are very common in the quantitative sciences, and describe finite difference schemes, solutions to problems in Markov processes…
Summation by parts is used to find the sum of a finite series of generalized harmonic numbers involving a specific polynomial or rational function. The Euler-Maclaurin formula for sums of powers is used to find the sums of some finite…
Several expansions of the solutions to the confluent Heun equation in terms of incomplete Beta functions are constructed. A new type of expansion involving certain combinations of the incomplete Beta functions as expansion functions is…
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. In general, the…
We consider the non-stationary Heun equation, also known as quantum Painlev\'e VI, which has appeared in different works on quantum integrable models and conformal field theory. We use a generalized kernel function identity to transform the…
In this paper we introduce the new class of generalized Volterra functions. We prove some integral representations for them via Fox-Wright H-functions and Meijer G-functions. From positivity conditions on the weight in these…
Recently, the degenerate gamma functions are introduced as a degenerate version of the usual gamma function by Kim-Kim. In this paper, we investigate several properties of them. Namely, we obtain an analytic continuation as a meromorphic…
This paper addresses new results on the factorization of the general Heun's operator, extending the investigations performed in previous works [{\it Applied Mathematics and Computation} {\bf 141} (2003), 177 - 184 and {\bf 189} (2007), 816…
We introduce matching functions as a means of summing heavy-quark logarithms to any order. Our analysis is based on Witten's approach, where heavy quarks are decoupled one at a time in a mass-independent renormalization scheme. The outcome…
As a generalization of Riemann-Liouville integral, we introduce integral transformations of convergent power series which can be applied to hypergeometric functions with several variables.
In many ways the solution to the Hedin equations represents an exact solution to the many body problem. However, for most systems of practical interest, the solution to the Hedin equations is rendered nearly numerically intractable because…
We have found an exact formula expressing a general correlation function containing both products and ratios of characteristic polynomials of random Hermitian matrices. The answer is given in the form of a determinant. An essential…