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In this paper we deal with a general type of integral formulas of the visual angle, among them those of Crofton, Hurwitz and Masotti, from the point of view of Integral Geometry. The purpose is twofold: to provide an interpretation of these…

Special cases of Weber-Schafheitlin type integrals are evaluated analytically.

In this paper, we introduce formal sine functions whose coefficients are elements of a generalized harmonic algebra and investigate their properties corresponding to the classical addition formula and Pythagorean theorem. By taking their…

A new heuristic method for the evaluation of definite integrals is presented. This method of brackets has its origin in methods developed for the evaluation of Feynman diagrams. The operational rules are described and the method is…

We extend the notion of regularized integrals introduced by Li-Zhou that aims to assign finite values to divergent integrals on configuration spaces of Riemann surfaces. We then give cohomological formulations for the extended notion using…

We derive the bilateral estimates for the module of continuity of the fractional integrals and derivatives for the functions from the classical Lebesgue-Riesz spaces.

In this note we derive some interesting definite integrals involving Malmsten logarithm forms, reciprocal logarithm forms and K\"{o}lbig type integrals in terms of special functions.

A recursion formula is derived which allows to evaluate invariant integrals over the orthogonal group O(N), where the integrand is an arbitrary finite monomial in the matrix elements of the group. The value of such an integral is…

This course on Feynman integrals starts from the basics, requiring only knowledge from special relativity and undergraduate mathematics. Topics from quantum field theory and advanced mathematics are introduced as they are needed. The course…

We consider a rational elliptic surface with a relatively minimal fibration. We compute the number of integral sections in the above rational elliptic surface. As an application, we obtain an estimate of polynomial solutions of some…

We study the integral transform which appeared in a different form in Akhiezer's textbook "Lectures on Integral Transforms".

We report the three main ingredients to calculate three- and four-electron integrals over Gaussian basis functions involving Gaussian geminal operators: fundamental integrals, upper bounds, and recurrence relations. In particular, we…

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 present a criterion that provides an easy sufficient condition in order that a collection of Abelian integrals has the Chebyshev property. This condition involves the functions in the integrand of the Abelian integrals and can be…

In this paper we provide a complete algebraic characterization of elementary equivalence of rings with a finitely generated additive group in the language of pure rings. The rings considered are arbitrary otherwise.

On June 15, 1876, the Proceedings of the Royal Society of London published a paper by Mr. W. H. L. Russell entitled "On certain integrals". The paper starts with "The following are certain integrals which will, I hope, be found…

Using formulas for certain quantities involving stable vectors, due to I. Molchanov, and in some cases utilizing the so-called divide and color model, we prove that certain families of integrals which, ostensibly, depend on a parameter are…

For the first time, a general fractional calculus of arbitrary order was proposed by Yuri Luchko in the works Mathematics 9(6) (2021) 594 and Symmetry 13(5) (2021) 755. In these works, the proposed approaches to formulate this calculus are…

We classify essential algebras whose irredundant non-refinable covers consist of primal algebras. The proof is obtained by constructing one to one correspondence between such algebras and partial orders on finite sets. Further, we prove…

The authors in \cite{alikhani} have given two examples to illustrate their results in which they have been eliminated the technical details. However, the authors in \cite{salahshur} claimed that the examples are incorrect. In fact they…