相关论文: On a q-analogue of the multiple gamma functions

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…

We present some completely monotonic functions involving the $q$-gamma function that are inspired by their analogues involving the gamma function.

In this article we give a proof of a q-analogue of the celebrated four functions theorem. This analogue was conjectured by Bjorner and includes as special cases both the four functions theorem and also Bjorner's q-analogue of the FKG…

We study three different $q$-analogues of the harmonic numbers. As applications, we present some generating functions involving number theoretical functions and give the $q$-generalization of Gosper's exponential generating function of…

A new $q$-analogue of Appell polynomial sequences and their generalizations are introduced and their main characterizations are proved. As consequences new $q$-analogue of Bernoulli and Euler polynomials and numbers is introduced, their…

We present some completely monotonic functions involving the$q$-polygamma functions, our result generalizes some known results.

In this paper, we introduce $q$-analogues of the Barnes multiple zeta functions. We show that these functions can be extended meromorphically to the whole plane, and moreover, tend to the Barnes multiple zeta functions when $q\uparrow 1$…

We give an asymptotic expansion (the higher Stirling formula) and an infinite product representation (the Weierstrass product formula) of the Vign\'{e}ras multiple gamma function by considering the classical limit of the multiple q-gamma…

We aim to introduce a new extension of Mittag-Leffler function via q-analogue and obtained their significant properties including integral representation, q-differentiation, q-Laplace transform, image formula under q-derivative operators.…

The connection between q-analogs of special functions and representations of quantum algebras has been developed recently. It has led to advances in the theory of q-special functions that we here review.

From two q-summation formulas we deduce certain series expansion formulas involving the q-gamma function. With these formulas we can give q-analogues of series expansions for certain constants.

We shall define the q-analogs of multiple zeta functions and multiple polylogarithms in this paper and study their properties, based on the work of Kaneko et al. and Schlesinger, respectively.

We give a q-analogue of Gauss' divisibility theorem

In this, paper we obtain a q-analogue of a double inequality involving the Euler gamma function which was first proved geometrically by Alsina and Tomas and then analytically by Sandor

In the present article, we introduce a $(p,q)$-analogue of the poly-Euler polynomials and numbers by using the $(p,q)$-polylogarithm function. These new sequences are generalizations of the poly-Euler numbers and polynomials. We give…

In this paper, we present the (p; q)-analogues of some inequalities concerning the digamma function. Our results generalize some earlier results.

We prove some properties of completely monotonic functions and apply them to obtain results on gamma and $q$-gamma functions.

We introduce new generalizations of the Gamma and the Beta functions. Their properties are investigated and known results are obtained as particular cases.

We give an asymptotic expansion (the higher Stirling formula) and an infinite product representation (the Weierstrass product representation) of the Vign\'{e}ras multiple gamma functions by considering the classical limit of the multiple…

Two integral representations of q-analogues of the Hurwitz zeta function are established. Each integral representation allows us to obtain an analytic continuation including also a full description of poles and special values at…