Related papers: Numerical Evaluation of Generalized Hypergeometric…

Motivated by the substantial development of the special functions, we contribute to establish some rigorous results on the general series identities with bounded sequences and hypergeometric functions with different arguments, which are…

In this paper, we propose a parametrised factor that enables inference on Gaussian networks where linear dependencies exist among the random variables. Our factor representation is effectively a generalisation of traditional Gaussian…

By means of inversion techniques and several known hypergeometric series identities, summation formulas for Fox-Wright function are explored. They give some new hypergeometric series identities when the parameters are specified.

We elaborate on the expansion of hypergeometric functions about rational parameters, where we focus mainly on the integer and half-integer case. The strategy and the basic steps of a recently developed algorithm for the expansion about…

The generalized Fermi-Dirac functions and their derivatives are important in evaluating the thermodynamic quantities of partially degenerate electrons in hot dense stellar plasmas. New recursion relations of the generalized Fermi-Dirac…

We describe a uniform way of obtaining basic hypergeometric functions as limits of the elliptic beta integral. This description gives rise to the construction of a polytope with a different basic hypergeometric function attached to each…

We construct an explicit orthonormal basis of piecewise ${}_{i+1}F_{i}$ hypergeometric polynomials for the Alpert multiresolution analysis. The Fourier transform of each basis function is written in terms of ${}_2F_3$ hypergeometric…

In a previous work ([Eb]), the author proposed a method employing contiguity relations to derive hypergeometric series in closed form. In [Eb], this method was used to derive Gauss's hypergeometric series $_2F_1$ possessing closed forms.…

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 provide new formulae for the degenerations of the bilateral basic hypergeometric function ${}_1\psi_1 ( a; b; q, z )$ with using the $q$-Borel-Laplace transformation. These are thought of as the first step to construct connection…

In this paper, we obtain recursion formulas for the Kamp\'e de Fe\'riet hypergeometric matrix function. We also give finite and infinite summation formulas for the Kamp\'e de Fe\'riet hypergeometric matrix function.

We examine hypergeometric functions in the finite field, p-adic and classical settings. In each setting, we prove a formula which splits the hypergeometric function into a sum of lower order functions whose arguments differ by roots of…

We introduce the notion of the generalized-analytical function of the poly-number variable, which is a non-trivial generalization of the notion of analytical function of the complex variable and, therefore, may turn out to be fundamental in…

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…

Various methods to obtain the analytic continuation near $z=1$ of the hypergeometric series $_{p+1}F_p(z)$ are reviewed together with some of the results. One approach is to establish a recurrence relation with respect to $p$ and then,…

Feynman integrals that have been evaluated in dimensional regularization can be written in terms of generalized hypergeometric functions. It is well known that properties of these functions are revealed in the framework of intersection…

Investigation of the generalized trigonometric and hyperbolic functions containing two parameters has been a very active research area over the last decade. We believe, however, that their monotonicity and convexity properties with respect…

In this paper we investigate the Meijer's $G$ function $G^{p,1}_{p+1,p+1}$ which for certain parameter values represents the Riemann-Liouville fractional integral of Meijer-N{\o}rlund function $G^{p,0}_{p,p}$. Our results for…

Using techniques in logarithmic geometry, we construct a logarithmic analogue of the Fulton--MacPherson configuration spaces. We similarly construct a logarithmically smooth degeneration of the Fulton--MacPherson configuration spaces. Both…

We present an efficient implementation of hypergeometric functions in arbitrary-precision interval arithmetic. The functions ${}_0F_1$, ${}_1F_1$, ${}_2F_1$ and ${}_2F_0$ (or the Kummer $U$-function) are supported for unrestricted complex…