Related papers: Some integrals involving the Stieltjes constants
Stieltjes boundary problems generalize the customary class of well-posed two-point boundary value problems in three independent directions, regarding the specification of the boundary conditions: (1) They allow more than two evaluation…
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 provide sufficient conditions under which the Catalan-like numbers are Stieltjes moment sequences. As applications, we show that many well-known counting coefficients, including the Bell numbers, the Catalan numbers, the central binomial…
We find sharp constants in the symmetric integral form of the John-Nirenberg inequality. The result is based upon computation of a new interesting Bellman function.
We present a new type of integral that is supposed to extend the usability of the Lebesgue integral in certain types of investigations. It is based on the Hausdorff dimension and measure. We examine the basic properties of the integral and…
A new simple proof of Stirling's formula via the partial fraction expansion for the tangent function is presented.
A number of new definite integrals involving Bessel functions are presented. These have been derived by finding new integral representations for the product of two Bessel functions of different order and argument in terms of the generalized…
We prove new results on the existence of positive solutions for some impulsive differential equation subject to nonlocal boundary conditions. Our boundary conditions involve an affine functional given by a Stieltjes integral. These cover…
The work studies some Difference equations, which are connected with Mejer's function.
In this paper we study the strong matrix Stieltjes moment problem. We obtain necessary and sufficient conditions for its solvability. An analytic description of all solutions of the moment problem is derived. Necessary and sufficient…
In this work we establish a theory of Calculus based on the new concept of displacement. We develop all the concepts and results necessary to go from the definition to differential equations, starting with topology and measure and moving on…
In this paper, we investigate a novel form of approximate orthogonality that is based on integral orthogonality. Additionally, we establish the fundamental properties of this new approximate orthogonality and examine its capability to…
In this note, we establish new an inequality of Ostrowski-type for double integrals involving functions of two independent variables by using fairly elementary analysis.
In this research, Minkowski type functions which are constructed on certain probability distributions, are introduced. There are investigated differential, integral, and other properties of these functions.
In this article it is proven the existence of integration of indefinite integrals as infinite derivative's series expansion. This also opens a new way to integrate a definite integral.
We show how two change-of-variables formulae for Lebesgue-Stieltjes integrals generalize when all continuity hypotheses on the integrators are dropped. We find that a sort of "mass splitting phenomenon" arises.
The present status of the (JR) dynamical parton distribution functions is reported. Different theoretical improvements, including the determination of the strange sea input distribution, the treatment of correlated errors and the inclusion…
In the paper, some lower bounds for polygamma functions are refined.
This paper is devoted to stability results for the Gaussian logarithmic Sobolev inequality, with explicit stability constants.
The Stieltjes constants $\gamma_n$ appear in the coefficients in the Laurent expansion of the Riemann zeta function $\zeta(s)$ about the simple pole $s=1$. We present an asymptotic expansion for $\gamma_n$ as $n\rightarrow \infty$ based on…