Related papers: Notes on the historical bibliography of the gamma …
In this article, we explore a series of elementary yet insightful results involving integrals related to Gaussian sums. Using techniques rooted in classical calculus, we derive several identities and evaluate nontrivial definite integrals…
A series transformation idea inspired by a formula of R. W. Gosper and some asymptotic expansions for the central binomial coefficients leads us to new accurate approximations for the Gamma function.
This is the classical monograph on the combinatorial study of Eulerian polynomials, published in 1970. It has been retyped in TeX and made available on the web with the kind permission of Springer-Verlag. This on-line version has an ouput…
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…
Recently, many researchers devoted their attention to study the extensions of the gamma and beta functions. In the present work, we focus on investigating some approximations for a class of Gauss hypergeometric functions by exploiting…
This paper discusses the incomplete Gamma and Beta integrals involving the generalised hypergeometric function. The distribution of the largest and the smallest roots of a ratio arising in comparing the mean differences among groups is…
Scholarly usage data provides unique opportunities to address the known shortcomings of citation analysis. However, the collection, processing and analysis of usage data remains an area of active research. This article provides a review of…
This communication shows the track for finding a solution for a sin(kx)/k**2 series and a fresh representation for the Euler's Gamma function in terms of Riemann's Zeta function. We have found a new series expression for the logarithm as a…
Motivated by open questions in the papers " Refinements and sharpenings of some double inequalities for bounding the gamma function" and "Complete monotonicity and monotonicity of two functions defined by two derivatives of a function…
Fracture functions and their evolution equations are reviewed. Some phenomenological applications are briefly discussed.
In this paper, we establish the irrationality of some open problems in mathematics based on using a recursive formula that generate the complete sequence of numbers. see [1] But before getting into that we begin with some Ramanujan notable…
The aim of this paper is to give the text of a recent introduction to nonlinear generalized functions exposed in my talk in the congress gf2011, which was asked by several participants. Three representative topics were presented: two…
The recurrence matrix relations, differentiation formulas, and analytical and fractional integral properties of incomplete gamma matrix functions $\gamma(Q, x)$ and $\Gamma(Q, x)$ are all covered in this article. The generalized incomplete…
We establish sharp inequalities involving the incomplete Beta and Gamma functions. These inequalities arise in the approximation of generalized Bernstein functions by higher order Thorin-Bernstein functions. Furthermore, new properties of a…
In this series of seven papers, predominantly by means of elementary analysis, we establish a number of identities related to the Riemann zeta function. Whilst this paper is mainly expository, some of the formulae reported in it are…
We have performed analytically the transverse momentum integrations in the real corrections to the longitudinal \gamma^*_L impact factor and carried out numerically the remaining integrations. I outline the analytical integration and…
We present some completely monotonic functions involving the $q$-gamma function that are inspired by their analogues involving the gamma function.
We introduce a new factorial function which agrees with the usual Euler gamma function at both the positive integers and at all half-integers, but which is also entire. We describe the basic features of this function.
Problems for evaluation and impact of published scientific works and their authors are discussed. The role of citations in this process is pointed out. Different bibliometric indicators are reviewed in this connection and ways for…
In this chapter we present an overview of the main ideas and methods in the fractional integration and cointegration literature. We do not attempt to give a complete survey of this enormous literature, but rather a more introductory…