Related papers: Numerical and graphical exploration of the general…
In this work we derive and evaluate some infinite integrals involving the product of a generalized logarithm and polynomial functions in the denominator. These integrals are expressed in terms of finite series involving the Hurwitz-Lerch…
Recent innovations on the differential calculus for functions of non-commuting variables, begun for a quaternionic variable, are now extended to the case of a general matrix over the complex numbers. The expansion of F(X+Delta) is given to…
We generalize previous definitions of Tesler matrices to allow negative matrix entries and negative hook sums. Our main result is an algebraic interpretation of a certain weighted sum over these matrices, which we call the Tesler function.…
In this paper, we investigate the Euler-type integral representations for the generalized hypergeometric matrix function and develop some transformations in terms of hypergeometric matrix functions. Furthermore, unit and half arguments have…
This paper generalizes beta divergence beyond its classical form associated with power variance functions of Tweedie models. Generalized form is represented by a compact definite integral as a function of variance function of the…
The generalised Gegenbauer functions of fractional degree (GGF-Fs), denoted by ${}^{r\!}G^{(\lambda)}_\nu(x)$ (right GGF-Fs) and ${}^{l}G^{(\lambda)}_\nu(x)$ (left GGF-Fs) with $x\in (-1,1),$ $\lambda>-1/2$ and real $\nu\ge 0,$ are special…
Linear algebra's main concerns are sets of vectors, linear functions, subspaces, linear systems, matrices and concepts about those, such as whether the solution of linear system exists or is unique; a set of vectors is linearly independent…
The incomplete beta function is an important special function in statistics. In modern theory of hypergeometric functions, we regard hypergeometric functions as pairings of twisted cycles and twisted cocycles. However, the incomplete beta…
Using a probabilistic approach, we derive some interesting combinatorial identities involving gamma and beta functions. These results generalize certain well-known combinatorial identities involving binomial coefficients and special…
Matrix functions with potential applications have a major role in science and engineering. One of the fundamental matrix functions, which is particularly important due to its connections with certain matrix differential equations and other…
Let $M(\alpha)$ denote the (logarithmic) Mahler measure of the algebraic number $\alpha$. Dubickas and Smyth, and later Fili and the author, examined metric versions of $M$. The author generalized these constructions in order to associate,…
In this paper, we introduce and share the new concept of $\mathcal{MT}(\lambda )$-functions and its some characterizations.
We introduce and solve an infinite class of loop integrals which generalises the well-known ladder series. The integrals are described in terms of single-valued polylogarithmic functions which satisfy certain differential equations. The…
We generalize the well-known mean value inequality of subharmonic functions for a slightly more general function class. We also apply this generalized mean value inequality to weighted boundary behavior and nonintegrability questions of…
We give closed-form expressions for the Dirichlet beta function at even positive integers and for the Dirichlet lambda function at odd positive integers, based on the function J(s) defined via convergent integral. We also show fundamental…
We give an overview of the development of algebras of generalized functions in the sense of Colombeau and recent advances concerning diffeomorphism invariant global algebras of generalized functions and tensor fields. We furthermore provide…
In this paper, we aim to present new extensions of incomplete gamma, beta, Gauss hypergeometric, confluent hypergeometric function and Appell-Lauricella hypergeometric functions, by using the extended Bessel function due to Boudjelkha [4].…
The multiple gamma functions of BM (Barnes-Milnor) type and the $q$-multiple gamma functions have been studied independently. In this paper, we introduce a new generalization of the multiple gamma functions called the $q$-BM multiple gamma…
This paper investigates the classical Gurland ratio of the gamma function and introduces its modified form, $\mathcal{G}^{\star}(x,y)$, which is particularly amenable to analytic expansions. By utilizing the Weierstrass product…
We investigate subclasses of generalized Bernstein functions related to complete Bernstein and Thorin-Bernstein functions. Representations in terms of incomplete beta and gamma as well as hypergeometric functions are presented. Several…