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We prove a master theorem for hypergeometric functions of Karlsson-Minton type, stating that a very general multilateral U(n) Karlsson-Minton type hypergeometric series may be reduced to a finite sum. This identity contains the…

Classical Analysis and ODEs · Mathematics 2007-05-23 Hjalmar Rosengren

It is known that a large class of integrable hydrodynamic type systems can be constructed through the Lauricella function, a generalization of the classical Gauss hypergeometric function. In this paper, we construct novel class of…

Exactly Solvable and Integrable Systems · Physics 2016-11-03 Y. Kodama , B. Konopelchenko

Let M be a smooth complex projective variety, bearing a K\"ahler symplectic form \omega and a Hamiltonian action of a torus T, with finitely many fixed points M^T. One standard form of the Duistermaat-Heckman theorem gives a formula for M's…

Symplectic Geometry · Mathematics 2022-02-04 Allen Knutson

The multiplicate form of Gould--Hsu's inverse series relations enables to investigate the dual relations of the Chu-Vandermonde-Gau{\ss}'s, the Pfaff-Saalsch\"utz's summation theorems and the binomial convolution formula due to Hagen and…

Combinatorics · Mathematics 2013-11-19 Christian Lavault

The paper is a survey of recent results in analysis of additive functions over function fields motivated by applications to various classes of special functions including Thakur's hypergeometric function. We consider basic notions and…

Number Theory · Mathematics 2007-05-23 Anatoly N. Kochubei

We prove several identities relating three-variable Mahler measures to integrals of inverse trigonometric functions. After deriving closed forms for most of these integrals, we obtain ten explicit formulas for three-variable Mahler…

Number Theory · Mathematics 2007-05-23 Mathew D. Rogers

We obtain certain Mellin-Barnes integrals which present wave functions for $GL(n,\mathbb{R})$ hyperbolic Sutherland model with arbitrary positive coupling constant.

Mathematical Physics · Physics 2021-08-17 S. Kharchev , S. Khoroshkin

In this paper, we investigate the determinants involving some trigonometric functions. We establish a connection between these determinants and the special values of Dirichlet L-functions, thereby extending Guo's results to arbitrary…

Number Theory · Mathematics 2025-12-23 Liwen Gao , Xuejun Guo

In the first part of this paper, we express the generalized Bessel function associated with dihedral systems and a constant multiplicity function as a infinite series of confluent Horn functions. The key ingredient leading to this…

Classical Analysis and ODEs · Mathematics 2020-09-02 Luc Deleaval , Nizar Demni

This article studies the monotonicity, log-convexity of the modified Lommel functions by using its power series and infinite product representation. Same properties for the ratio of the modified Lommel functions with the Lommel function,…

Classical Analysis and ODEs · Mathematics 2017-04-18 Saiful R Mondal

With the increasing importance of the Mittag-Leffler function in the physical applications, these days many researchers are studying various generalizations and extensions of the Mittag-Leffler function. In this paper efforts are made to…

Complex Variables · Mathematics 2021-07-20 Ritu Agarwal , Urvashi Purohit Sharma , Ravi P. Agarwal

In a prior paper we found that the Fourier-Legendre series of a Bessel function of the first kind J_{N}\left(kx\right) and of a modified Bessel functions of the first kind I_{N}\left(kx\right) lead to an infinite set of series involving…

General Mathematics · Mathematics 2026-01-21 Jack C. Straton

In this work, Miller Ross function with bicomplex arguments has been introduced. Various properties of this function including recurrence relations, integral representations and differential relations are established. Furthermore, the…

Complex Variables · Mathematics 2024-08-26 Snehasis Bera , Sourav Das , Abhijit Banerjee

In this paper, we establish Kronecker limit type formulas for the Mordell-Tornheim zeta function $\Theta(r,s,t,x)$ as a function of the second as well as the third arguments. As an application of these formulas, we obtain results of…

Number Theory · Mathematics 2025-01-03 Sumukha Sathyanarayana , N. Guru Sharan

We define a multiple Dirichlet series associated with quadrics which is the zero locus of a quadratic form. This multiple Dirichlet series is linked to a Shintani zeta function associated with a prehomogeneous vector space. To obtain the…

Number Theory · Mathematics 2024-01-12 Jun Wen

This manuscript introduces a generalization of the Mellin integral transform within the framework of weighted fractional calculus with respect to an increasing function. The proposed transform is much more suitable for working with…

Functional Analysis · Mathematics 2025-12-09 Gustavo Dorrego , Luciano Luque y Rubén Cerutti

The Mellin transform and several Dirichlet series related with the Riemann zeta function are used to deduce some identities similar to the classical M\"untz formula [4]. These formulas are derived in the critical strip and in the half-plane…

Classical Analysis and ODEs · Mathematics 2017-05-29 Hélder Lima

We consider mixed type multiple orthogonal polynomials associated with a system of weight functions consisting of two vectors. One vector is defined in terms of scaled modified Bessel function of the first kind $I_\mu$ and $I_{\mu+1}$, the…

Classical Analysis and ODEs · Mathematics 2016-09-28 Lun Zhang

The main result of this paper is the existence and uniqueness of solution of the Dirichlet problem for quaternionic Monge-Ampere equations in quaternionic strictly pseudoconvex bounded domains in H^n. We continue the study of the theory of…

Complex Variables · Mathematics 2016-07-06 Semyon Alesker

We calculate the fibre integrals of the hypersurface in a torus in the form of their Mellin transforms. Especially, our method works efficiently for an affine hypersurface defined by a so called simpliciable polynomial. The relations…

Algebraic Geometry · Mathematics 2007-05-23 Susumu Tanabé