Related papers: On the Barnes double gamma function

The functional equations of the Riemann zeta function, the Hurwitz zeta function, and the Lerch zeta function have been well known for a long time, and there is great importance in studying these zeta functions. For example, fundamental…

In this article, we define a special function called the Bigamma function. It provides a generalization of Euler's gamma function. Several algebraic properties of this new function are studied. In particular, results linking this new…

Using a variational approach, two new series representations for the incomplete Gamma function are derived: the first is an asymptotic series, which contains and improves over the standard asymptotic expansion; the second is a uniformly…

Motivated mainly by certain interesting recent extensions of the Gamma, Beta and hypergeometric functions, we introduce here new extensions of the Beta function, hypergeometric and confluent hypergeometric functions. We systematically…

The main object of this paper is to present generalizations of gamma, beta and hypergeometric functions. Some recurrence relations, transformation formulas, operation formulas and integral representations are obtained for these new…

We show a direct approach to Kinkelin's integral involving the cotangent function.

As one of the asymptotic formulas of the zeta-function, Hardy and Littlewood gave asymptotic formulas called the approximate functional equation. In this paper, we prove an approximate functional equation of the Barnes double zeta-function…

In the paper, the authors establish some asymptotic formulas and double inequalities for the factorial $n!$ and the gamma function $\Gamma$ in terms of the tri-gamma function $\psi'$.

We introduce an "$L$-function" $\mathcal{L}$ built up from the integral representation of the Barnes' multiple zeta function $\zeta$. Unlike the latter, $\mathcal{L}$ is defined on a domain equipped with a non-trivial action of a group $G$.…

In the paper, the authors establish three kinds of double inequalities for the trigamma function in terms of the exponential function to powers of the digamma function. These newly established inequalities extend some known results. The…

In this paper, we introduce the hypermultiple gamma functions of BM-type and prove the asymptotic expansion of these functions.

This manuscript introduces a general multisection identity expressed equivalently in terms of infinite double products and/or infinite double series, from which several new product or summation identities involving special functions…

We derive several identities for the Hurwitz and Riemann zeta functions, the Gamma function, and Dirichlet $L$-functions. They involve a sequence of polynomials $\alpha_k(s)$ whose study was initiated in an earlier paper. The expansions…

The two-fold aim of the paper is to unify and generalize on the one hand the double integrals of Beukers for $\zeta(2)$ and $\zeta(3),$ and those of the second author for Euler's constant $\gamma$ and its alternating analog $\ln(4/\pi),$…

An analysis of the zeta and gamma function is presented, using elementary functions like [] and {}, a general formula for the angle of zeta(1/2 + i*n) is found and the same for the gamma function.

In the paper, we present a monotonicity result of a function involving the gamma function and the logarithmic function, refine a double inequality for the gamma function, and improve some known results for bounding the gamma function.

As a generalization of the results [KW3],we study the functional equation of the higher Selberg zeta function for congruence subgroups. To obtain the gamma factor of this function, we introduce a higher Dirichlet $L$-function. Then we…

We intimate deeper connections between the Riemann zeta and gamma functions than often reported and further derive a new formula for expressing the value of $\zeta(2n+1)$ in terms of zeta at other fractional points. This paper also…

We aim to introduce a new extension of beta function and to study its important properties. Using this definition, we introduce and investigate new extended hypergeometric and confluent hypergeometric functions. Further, some hybrid…

The multiple gamma function $\Gamma_n$, defined by a recurrence-functional equation as a generalization of the Euler gamma function, was originally introduced by Kinkelin, Glaisher, and Barnes around 1900. Today, due to the pioneer work of…