Related papers: Derangements and the $p$-adic incomplete gamma fun…

The split involution quantization scheme, proposed previously for pure second--class constraints only, is extended to cover the case of the presence of irreducible first--class constraints. The explicit Sp(2)--symmetry property of the…

We revisit a representation for the Riemann zeta function $\zeta(s)$ expressed in terms of normalised incomplete gamma functions given by the author and S. Cang in Methods Appl. Anal. {\bf 4} (1997) 449--470. Use of the uniform asymptotics…

In the paper, the authors concisely survey and review some functions involving the gamma function and its various ratios, simply state their logarithmically complete monotonicity and related results, and find necessary and sufficient…

A new expansion for integral powers of the hypergeometric function corresponding to a special case of the incomplete beta function is summarized, and consequences, including two new sums involving digamma (psi) functions are presented.

We introduce Omega functions that generalize Euler Gamma functions and study the functional difference equation they satisfy. Under a natural exponential growth condition, the vector space of meromorphic solutions of the functional equation…

We consider the functional inverse of the Gamma function in the complex plane, where it is multi-valued, and define a set of suitable branches by proposing a natural extension from the real case.

We simplify the proof of some widely used theoretical theorems, extending their applicability, while correcting some erroneous results. We also generalize key results and present new results that contribute to the development of the theory.…

In this note, we present two new identities for derangements. As a corollary, we have a combinatorial proof of the irreducibility of the standard representation of symmetric groups.

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…

Some inequalities for the ratios of generalized digamma functions are presented. The approache makes use of the series representations of the $(q,k)$-digamma and $(p,q)$-digamma functions.

We show how infinite series of a certain type involving generalized harmonic numbers can be computed using a knowledge of symmetric functions and multiple zeta values. In particular, we prove and generalize some identities recently…

In the paper, necessary and sufficient conditions are presented for a function involving a ratio of gamma functions to be logarithmically completely monotonic. This extends and generalizes the main result in [\emph{Inequalities and…

In combinatorics, a derangement is a permutation that has no fixed points. The number of derangements of an n-element set is called the n-th derangement number. In this paper, as natural companions to derangement numbers and degenerate…

We describe some new general constructions of $p$-adic $L$-functions attached to certain arithmetically defined complex $L$-functions coming from motives over $\bold Q$ with coefficiens in a number field $T$, with $[T:\bold Q]<\infty$.…

An approach to build Probabilistic Arithmetic in which initial values of all correlated random variables are known, but with varying degrees of accuracy. As a result of the proposed Probabilistic Arithmetic operations, variable values,…

We give a survey of Denef's rationality theorem on $p$-adic integrals, its uniform in $p$ versions, the relevant model theory, and a number of applications to counting subgroups of finitely generated nilpotent groups and conjugacy classes…

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

Three types of integral representations for the cumulative distribution functions of convolutions of non-central p-variate gamma distributions are given by integration of elementary complex functions over the p-cube Cp =…

In this paper, we give explicit evaluation for some infinite series involving generalized (alternating) harmonic numbers. In addition, some formulas for generalized (alternating) harmonic numbers will also be derived.

We introduce a class of $2d$ sigma models which are parameterized by a function of one variable. In addition to the physical field $g$, these models include an auxiliary field $v_\alpha$ which mediates interactions in a prescribed way. We…