Related papers: Some integrals involving the Stieltjes constants
Cyclotomic polylogarithms are reviewed and new results concerning the special constants that occur are presented. This also allows some comments on previous literature results using PSLQ.
The Stieltjes constants gamma_k(a) are the expansion coefficients in the Laurent series for the Hurwitz zeta function about its only pole at s=1. We present the relation of gamma_k(1) to the eta_j coefficients that appear in the Laurent…
This paper extends the stability calculations carried out for a spherical particle [Eur. Phys. J. B, vol. 37 (2004) or arXiv: cond-mat/0401404] to the case of a cylindrical inclusion.
The Stieltjes constants $\gamma_k(a)$ appear as the coefficients in the regular part of the Laurent expansion of the Hurwitz zeta function $\zeta(s,a)$ about $s=1$. We present the evaluation of $\gamma_1(a)$ and $\gamma_2(a)$ at rational…
The Stieltjes constants have attracted considerable attention in recent years and a number of authors, including the present one, have considered various ways in which these constants may be evaluated. The primary purpose of this paper is…
We find Stieltjes-type and Jacobi-type continued fractions for some "master polynomials" that enumerate permutations, set partitions or perfect matchings with a large (sometimes infinite) number of simultaneous statistics. Our results…
This article describes some aspects of Cauchy integrals and related geometry of sets and measures in Euclidean spaces, etc.
This paper uses differential spaces to obtain some new results in integrable Hamiltonian systems
The purpose of this article is twofold. First, we introduce the constants $\zeta_k(\alpha,r,q)$ where $\alpha \in (0,1)$ and study them along the lines of work done on Euler constant in arithmetic progression $\gamma(r,q)$ by Briggs,…
In this paper, new integral representations for the Bessel $J$ and $I$ functions were presented and their results were used to derive an expression for the Modified Bessel $K$ function.
The close form of some integrals involving recently developed generalized k-Struve functions is obtained. The outcome of these integrations is expressed in terms of generalized Wright functions. Several special cases are deduced which lead…
Using the notion of the truncated variation we obtain a new theorem on the existence and estimation of the Riemann-Stieltjes integral. As a special case of this theorem we obtain an improved version of the Lo\'{e}ve-Young inequality for the…
We study the question, whether a Riemann-Stieltjes integral of a positive continuous function with respect to a non-negative function of bounded variation is positive.
Multiple scalar integral representations for traces of operator derivatives are obtained and applied in the proof of existence of the higher order spectral shift functions.
The Stieltjes classes play a significant role in the moment problem since they permit to expose an infinite family of probability distributions all having equal moments of all orders. Given a moment-indeterminate distribution, it may not be…
Orthogonal polynomials of several variables have a vector-valued three-term recurrence relation, much like the corresponding one-dimensional relation. This relation requires only knowledge of certain recurrence matrices, and allows simple…
We give an alternative definition of integral at the generality of the Perron integral and propose an exposition of the foundations of integral theory starting from this new definition. Both definition and proofs needed for the development…
The present paper contains a generalization of some interpolation theorems of S. A. Vinogradov.
In this paper, we present several novel integral representations of Catalan's constant. We begin by deriving an initial result expressed as a double integral. Subsequently, as a consequence of this result, we establish a general theorem…
In the framework of continued fraction expansions of Stieltjes transforms, we consider shifting of semicircular laws. The continuous part of the associated measure admits a density function which is the quotient of semicircular one by a…