Related papers: A binomial formula for evaluating integrals
A modified Gauss's algorithm for solving a system of linear equations in an integral ring is proposed, as well as an appropriate algorithm for calculating the elements of the adjoint matrix.
In a previous paper a new approach has been introduced for computing, recursively and numerically, one-loop tensor integrals. Here we describe a few modifications of the original method that allow a more efficient numerical implementation…
We present several sequences involving harmonic numbers and the central binomial coefficients. The calculational technique is consists of a special summation method that allows, based on proper two-valued integer functions, to calculate…
An operatorial method, already employed to formulate a generalization of the Ramanujan master theorem, is applied to the evaluation of integrals of various type. This technique provide a very flexible and powerful tool yielding new results…
By combining the telescoping method with an algebraic relation, four classes of binomial moments are examined. Several explicit summation formulae are established.
The Fourier transform is naturally defined for integrable functrions. Otherwise, it should be stipulated in which sense the Fourier transform is understood. We consider some class of radial and, generally saying, nonintegrable functions.…
We give an exact coefficients formula of any infinite product of power series with constant term equal to $1$, by using structures from partitions of integers and permutation groups. This is an universal theorem for various of Binomial-type…
In our previous paper an effective algorithm for inverting polynomial automorphisms was proposed. We extend its application to the case of formal power series over a field of arbitrary characteristic and illustrate the proposed approach…
Recently, Bovadzhiev studied a power series whose coefficients are binomial expressions and extended some known formulas involving classical special functions and polynomials. The aim of this paper is to adopt his ideas to express several…
In this paper, we find an elementary approach for double sums where the inner sum is binomial but incomplete. We apply our core identity and its relatives to double sums involving famous numbers such as harmonic numbers, Fibonacci numbers,…
In this paper, we propose a new method for calculating integrals for a special class of integrands. As an application, we show how this method can be used to derive optimal pointwise temporal estimates for a class of nonlocal evolution…
We introduce and prove evaluations for families of multiple elliptic integrals by solving special types of ordinary and partial differential equations. As an application, we obtain new expressions of Ramanujan-type series of level 4 and…
In this note, we derive a finite summation formula and an infinite summation formula involving Harmonic numbers of order up to some order by means of several definite integrals
In this study, new master theorems and general formulas of integrals are presented and implemented to solve some complicated applications in different fields of science. The proposed theorems are considered to be generators of new problems,…
In the present article, we study Bell based Euler polynomial of order {\alpha} and investigate some useful correlation formula, summation formula and derivative formula. Also, we introduce some relation of string number of the second kind.…
Using matrix inversion and determinant evaluation techniques we prove several summation and transformation formulas for terminating, balanced, very-well-poised, elliptic hypergeometric series.
In this work, Miller Ross function with bicomplex arguments has been introduced. Various properties of this function including recurrence relations, integral representations and differential relations are established. Furthermore, the…
In this paper, we obtain some formulae for harmonic sums, alternating harmonic sums and Stirling number sums by using the method of integral representations of series. As applications of these formulae, we give explicit formula of several…
In the paper we analyse the exact solutions to scalar PDEs obtained thanks to summable Taylor series provided by Adomian's decomposition method. We propose the modification of the method which makes the calculations of Taylor coefficients…
In the paper we present some new inversion formulas and two new formulas for Stirling numbers.