Related papers: Some Parseval-Goldstein Type Theorems For Generali…
We study various Stieltjes integrals as Poisson-Stieltjes, conjugate Poisson-Stieltjes, Schwartz-Stieltjes and Cauchy-Stieltjes and prove theorems on the existence of their finite angular limits a.e. in terms of the singular…
In this paper, we establish an identity for Bernoulli's generalized polynomials. We deduce generalizations for many relations involving classical Bernoulli numbers or polynomials. In particular, we generalize a recent Gessel identity.
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…
It is known that Struve function $\mathbf H_\nu$ and modified Struve function $\mathbf L_\nu$ are closely connected to Bessel function of the first kind $J_\nu$ and to modified Bessel function of the first kind $I_\nu$ and possess…
Motivated by the substantial development of the special functions, we contribute to establish some rigorous results on the general series identities with bounded sequences and hypergeometric functions with different arguments, which are…
First some definite integrals of W. H. L. Russell, almost all with trigonometric function integrands, are derived, and many generalized. Then a list is given in Russell-style of generalizations of integral identities of Amdeberhan and Moll.…
The connection between derivatives of $L(s,f)$ for periodic arithmetical functions $f$ at $s=1$ and generalized Stieltjes constants has been noted earlier. In this paper, we utilize this link to throw light on the arithmetic nature of…
New identity for fractional integrals have been defined. By using of this identity, we obtained new estimates on generalization of Hadamard, Ostrowski and Simpson type inequalities for s-convex, quasi-convex, m-convex functions via Riemann…
We study the space of generalized translation invariant valuations on a finite-dimensional vector space and construct a partial convolution which extends the convolution of smooth translation invariant valuations. Our main theorem is that…
Miller-Paris transformations are extensions of Euler's transformations for the Gauss hypergeometric functions to generalized hypergeometric functions of higher-order having integral parameter differences (IPD). In our recent work we…
The difference between the quadratic L-groups L_*(A) and the symmetric L-groups L^*(A) of a ring with involution A is detected by generalized Arf invariants. The special case A=Z[x] gives a complete set of invariants for the Cappell…
This research note deals with the evaluation of some generalized beta-type integral operators involving the multi-index Mittag-Leffler function $E_{\epsilon_{i}),(\omega_{i})}(z)$. Further, we derive a new family of beta-type integrals…
In this note, we recall Kummer's Fourier series expansion of the 1-periodic function that coincides with the logarithm of the Gamma function on the unit interval $(0,1)$, and we use it to find closed forms for some numerical series related…
This paper discusses generalizations of logarithmic and hyperbolic integrals. A new proof for an integral presented by Vardi and several other integrals in relation to known mathematical constants are discovered. We introduce the signed…
We generalize Lindemann-Weierstrass theorem and Gelfond -Schneider-Baker Theorem. We find new transcendental numbers in this work. There are several methods to find transcendental numbers in the work. Recently transcendental numbers are…
In this paper, new identity for fractional integrals have been defined. By using of this identity, we obtained new general inequalities containing all of Hadamard, Ostrowski and Simpson type inequalities for for functions whose derivatives…
In this paper, some new inequalities of Ostrowski type established for the class of m- and (alpha,m)-geometrically convex functions which are generalizations of geometric convex functions.
Gei\ss-Leclerc-Schr\"oer [Invent. Math. 209 (2017)] has introduced a notion of generalized preprojective algebra associated with a generalized Cartan matrix and its symmetrizer. This class of algebra realizes a crystal structure on the set…
In this paper, we investigate the Euler-type integral representations for the generalized hypergeometric matrix function and develop some transformations in terms of hypergeometric matrix functions. Furthermore, unit and half arguments have…
We construct a Moutard-type transform for the generalized analytic functions. The first theorems and the first explicit examples in this connection are given.