相关论文: Some integrals involving the Stieltjes constants:P…
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…
Sharp extensions of Pitt's inequality and bounds for Stein-Weiss fractional integrals are obtained that incorporate gradient forms and vector-valued operators. Such results include Hardy-Rellich inequalities.
In an earlier paper we introduced the notion of 'bifurcating continued fractions' in a heuristic manner. In this paper a formal theory is developed for the 'bifurcating continued fractions'.
The motive of this note is twofold. Inspired by the recent development of a new kind of Hardy inequality, here we discuss the corresponding Hardy-Rellich and Rellich inequality versions in the integral form. The obtained sharp Hardy-Rellich…
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 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 work, we investigate the one-dimensional heat equation within the framework of Stieltjes calculus. We first consider the equation associated with two fixed derivators and develop a constructive approach to establish the existence of…
In this paper, we consider the degenerate Stirling polynomials of the second kind which are derived from the generating function. In addition, we give some new identities for these polynomials.
By using Cauchy integral formula in the theory of complex functions, the authors establish some integral representations for the principal branches of several complex functions involving the logarithmic function, find some properties, such…
The generalized Stieltjes transform (GST) is an integral transform that depends on a parameter $\rho > 0$. In previous work a convenient form of the inverse transformation was derived for the case $\rho = 3/2$. This paper generalizes that…
Understanding sustainability through modeling involves one of the complex and interdisciplinary activities where mathematics plays a key role. We provide arguments favoring the need for developing global models for measuring the status of…
The generating function of Stieltjes-Carlitz polynomials is a solution of Heun's differential equation and using this relation Carlitz was the first to get exact closed forms for some Heun functions. Similarly the associated…
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…
Motivated by the limitations of the traditional definitions of the Riemann-Stieltjes and Darboux-Stieltjes integrals, we introduce a generalized Darboux-Stieltjes integral that is equivalent to an earlier generalization by Ross \cite{Ross}.…
This paper treat determinacy of strong moment problems in part I and indeterminacy of strong moment problems in part II. This paper is a summary of the following papers: [1] Ald\'en. E., Determinacy of Strong Moment Problems. [2] On…
The approximative theorems of incomplete Riemann-Stieltjes sums of Ito stochastic integral, mean square integral and Stratonovich stochastic integral with respect to Brownian motion are investigated. Some sufficient conditions of incomplete…
Generalized Stieltjes constants $\gamma$ n (a) are the coecients in the Laurent series for the Hurwitz-zeta function $\zeta$(s, a) at the pole s = 1. Many authors proved formulas for these constants. In this paper, using a recurrence…
There are new integrable cases due to the construction from the previous version.
This paper uses differential spaces to obtain some new results in integrable Hamiltonian systems
New index transforms, involving squares of Kelvin functions, are investigated. Mapping properties and inversion formulas are established for these transforms in Lebesgue spaces. The results are applied to solve a boundary value problem on…