相关论文: The multiple gamma functions and the multiple q-ga…

Euler's Gamma function $\Gamma$ either increases or decreases on intervals between two consequtive critical points. The inverse of $\Gamma$ on intervals of increase is shown to have an extension to a Pick-function and similar results are…

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

Let $(\Sigma_A, \sigma)$ be a subshift of finite type and let $M(x)$ be a continuous function on $\Sigma_A$ taking values in the set of non-negative matrices. We extend the classical scalar pressure function to this new setting and prove…

We provide new representations for the finite parts at the poles and the derivative at zero of the Barnes zeta function in any dimension in the general case. These representations are in the forms of series and limits. We also give an…

The problem of asymptotic expansions of Green functions in perturbative QFT is studied for the class of Euclidean asymptotic regimes. Phenomenological applications are analyzed to obtain a meaningful mathematical formulation of the problem.…

In this paper, we introduce and study multiple $\wp$-functions, which generalize the classical Weierstrass $\wp$-function to iterated sums over lattice points, and we establish explicit formulas expressing them in terms of single…

We identify a partition-theoretic generalization of Riemann zeta function and the equally positive integer-indexed harmonic sums at infinity, to obtain the generating function and the integral representations of the latter. The special…

We study q-integral representations of the q-gamma and the q-beta functions. This study leads to a very interesting q-constant. As an application of these integral representations, we obtain a simple conceptual proof of a family of…

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

The tau function corresponding to the affine ring of a certain plane algebraic curve, called (n,s)-curve, embedded in the universal Grassmann manifold is studied. It is neatly expressed by the multivariate sigma function. This expression is…

In this paper we derive a new representation for the incomplete gamma function, exploiting the reformulation of the method of steepest descents by C. J. Howls (Howls, Proc. R. Soc. Lond. A 439 (1992) 373--396). Using this representation, we…

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…

In this article, a characterization of the class of Herglotz-Nevanlinna functions in $n$ variables is given in terms of an integral representation. Furthermore, alternative conditions on the measure appearing in this representation are…

We consider multiply periodic functions, sometimes called Abelian functions, defined with respect to the period matrices associated with classes of algebraic curves. We realise them as generalisations of the Weierstras P-function using two…

Recently, Debruyne and Tenenbaum proved asymptotic formulas for the number of partitions with parts in $\mathcal{L}\subset\mathbb{N}$ ($\gcd(\mathcal{L})=1$) and good analytic properties of the corresponding zeta function, generalizing work…

In the present paper we introduce some expansions, based on the falling factorials, for the Euler Gamma function and the Riemann Zeta function. In the proofs we use the Fa\'a di Bruno formula, Bell polynomials, potential polynomials,…

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…

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.

E661 in the Enestrom index. This was originally published as "Variae considerationes circa series hypergeometricas" (1776). In this paper Euler is looking at the asymptotic behavior of infinite products that are similar to the Gamma…

We present the q-Stirling's formula using the q-product determined by Tsallis entropy as nonextensive generalization of the usual Stirling's formula. The numerical computations and the proof are also shown. Moreover, we derive and prove…