相关论文: More About Trigonometric Series and Integration
In the last decades, the theory of digamma function has been developed with a high impact of interest by many authors. Here, we established some interesting results for digamma function, and also we have computed the values of digamma…
This is a comment on the article "Integrable Systems in Stringy Gravity" by D. V. Gal'tsov, Phys. Rev. Lett. 74, 2863, (1995).
We evaluate binomial series with harmonic number coefficients, providing recursion relations, integral representations, and several examples. The results are of interest to analytic number theory, the analysis of algorithms, and…
In this paper we consider the question of existence of trigonometric series universal in weighted $L^1_{\mu}[0,2\pi]$ spaces with respect to rearrangements and in usual sense.
The problem of advancing coordinatization of mathematics is considered. The need to develop a theory for measuring value and complexity of mathematical implications and proofs is discussed including motivations, benefits and implementation…
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…
This is an overview of merging the techniques of Riesz space theory and convex geometry.
We investigate the inversion of perturbation series and its resummation, and prove that it is related to a recently developed parametric perturbation theory. Results for some illustrative examples show that in some cases series reversion…
This is an introductory review of the connection between homotopy theory and path integrals, mainly focus on works done by Schulman [23] that he compared path integral on SO(3) and its universal covering space SU(2), DeWitt and Laidlaw [15]…
The Integration Theory of Linear Ordinary Differential Equation.
These are notes on the theory of supermanifolds and integration on them, aiming to collect results that are useful for a better understanding of superstring perturbation theory in the RNS formalism.
Inclusion properties are studied for balls of the triangular ratio metric, the hyperbolic metric, the $j^*$-metric, and the distance ratio metric defined in the unit ball domain. Several sharp results are proven and a conjecture about the…
Classical Schur analysis is intimately connected to the theory of orthogonal polynomials on the circle [Simon, 2005]. We investigate here the connection between multipoint Schur analysis and orthogonal rational functions. Specifically, we…
The concept of uniform tangent sets was introduced and discussed in [3 - Krastanov, Ribarska, SIAM J. Control Optim., 55(3), 2017]. This study is devoted to their further investigation and to generalization of the abstract Lagrange…
In this paper, the improvement about the generalized Kolmogorov-type three series theorem, in the case of NQD random variables, is obtained by different method. Furthermore, the generalized Kolmogorov-type three series theorem is…
This paper provides a Liouville principle for integration in terms of dilogarithm and partial result for polylogarithm.
By dividing hypergeometric series representations of the inverse sine by sin^-1 (x) and integrating, new double series representations of integers and constants arise. Binomial coefficients and the sine integral are thus combined in double…
This is an English translation of the following paper, published several years ago: Nikonorov Yu.G. On the geodesic diameter of surfaces with involutive isometry (Russian), Tr. Rubtsovsk. Ind. Inst., 2001, V. 9, 62-65, Zbl. 1015.53041. All…
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…
Relations among integrals of logarithms, polylogarithms and Euler sums are presented. A unifying element being the introduction of Nielsen's generalized polylogarithms.