相关论文: Infinite Product Representations fot Multiple Gamm…

Using the representation of E_q(2) on the non-commutative space zz^*-qz^*z=\sigma; q<1, \sigma>0 summation formulas for the product of two, three and four q-Kummer functions are derived.

By starting with Durand's double integral representation for a product of two Jacobi functions of the second kind, we derive an integral representation for a product of two Jacobi functions of the second kind in kernel form. We also derive…

In this short note, we compute higher extension groups for all irreducible representations and deduce the multiplicity formula for finite length representations in triple product case.

This article provides a general expression for infinitely divisible multivariate gamma distributions defined by their Laplace transforms, as well as the conditional Laplace transform of infinitely divisible multivariate gamma…

Convergent infinite products, indexed by all natural numbers, in which each factor is a rational function of the index, can always be evaluated in terms of finite products of gamma functions. This goes back to Euler. A purpose of this note…

In this paper we will give a proof of a certain summation formula for Gamma functions utilizing Gegenbauer polynomials.

This paper shows that for a given irreducible representation $\rho$ of $\Gamma/\Gamma_1$, the two functions dim($M_k(\Gamma_1,\rho)$) and dim($S_k(\Gamma_1,\rho)$) of $k$ are almost linear functions.

In this paper, we derive a general formula to express the product of three theta functions as a linear combination of other products of three theta functions. Moreover, we use the main formula to deduce a general formula for the product of…

A GGC (Generalized Gamma Convolution) representation of Riemann's Xi-function is constructed.

We show convexity of solutions to a class of convex variational problems in the Gauss and in the Wiener space. An important tool in the proof is a representation formula for integral functionals in this infinite dimensional setting, that…

In recent years, Karr's difference field theory has been extended to the so-called $R\Pi\Sigma$-extensions in which one can represent not only indefinite nested sums and products that can be expressed by transcendental ring extensions, but…

Various approaches to the numerical representation of the Incomplete Gamma Function F_m(z) for complex arguments z and small integer indexes m are compared with respect to numerical fitness (accuracy and speed). We consider power series,…

In this paper, we study some extended hypergeometric functions from matrix point of view. We have given the integral representations of these matrix functions. Finally, we obtain some generating function relations using fractional…

Multiple zeta-star values are variants of multiple zeta values which allow equality in the definition. Similar to the theory of continued fractions, every real number which is greater than $1$ can be realized as an unique infinite multiple…

Using the log-convexity of the Gamma function and Euler's reflection formula, we give a new proof of a classical weighted sine product inequality. Two different parameter choices yield two competing upper bounds for the same product. We…

In 2021, Hu and Kim defined a new type of gamma function $\widetilde{\Gamma}(x)$ from the alternating Hurwitz zeta function $\zeta_{E}(z,x)$, and obtained some of its properties. In this paper, we shall further investigate the function…

We study unitary representations of semidirect products of a compact quantum group with a finite group. We give a classification of all irreducible unitary representations, a description of the conjugate representation of irreducible…

This paper presents a family of new integral representations and asymptotic series of the multiple gamma function. The numerical schemes for high-precision computation of the Barnes gamma function and Glaisher's constant are also discussed.

In this study, we derive the infinite product representation of the $\operatorname{sinc}(\mathrm{z})$ function by expressing it in a trigonometric form, evoking similarities to Morrie's Law and Euler's Product formula, along with their…

For a rational function of several variables with nonnegative imaginary part on the upper poly-half-plane, the matrix representations are obtained.