Related papers: Power series with inverse binomial coefficients an…
We calculate a double integral over a product of Legendre polynomials multiplied by a binomial raised to a power.
In this work, we explicitly compute the group inverse of symmetric and periodic Jacobi matrices.
This note gives a few rapidly convergent series representations of the sums of divisors functions. These series have various applications such as exact evaluations of some power series, computing estimates and proving the existence results…
We provide an alternative description of the group of Riordan arrays, by using two power series of the form $\sum_{n=0}^{\infty} g_n x^n$, where $g_0 \ne 0$ to build a typical element of the constructed group. We relate these elements to…
We compute correlation functions of inverse powers and ratios of characteristic polynomials for random matrix models with complex eigenvalues. Compact expressions are given in terms of orthogonal polynomials in the complex plane as well as…
Recent progress in analytical calculation of the multiple [inverse, binomial, harmonic] sums, related with epsilon-expansion of the hypergeometric function of one variable are discussed.
We present a versatile construction allowing one to obtain pairs of integer sets with infinite symmetric difference, infinite intersection, and identical representation functions.
In this paper, we find explicit formulas for higher order derivatives of the inverse tangent function. More precisely, we study polynomials which are induced from the higher-order derivatives of arctan(x). Successively, we give generating…
A class of bilinear permutation polynomials over a finite field of characteristic 2 was constructed in a recursive manner recently which involved some other constructions as special cases. We determine the compositional inverses of them…
In the research, with aid of the Fa\`a di Bruno formula, be virtue of several identities for the Bell polynomials of the second kind, with help of two combinatorial identities, by means of the (logarithmically) complete monotonicity of…
We continue our study on relationships between Fibonacci (Lucas) numbers and Bernoulli numbers and polynomials. The derivations of our results are based on functional equations for the respective generating functions, which in our case are…
We give a generating function for the number of unimodal permutations with a given cycle structure.
Abstract. We generalize the $b$-ary binomial coefficients with negative entries, which is based on the generating function obtained in early work. Besides an explicit expression involving the restricted partition, several properties such as…
The central binomial series at negative integers are expressed as a linear combination of values of certain two polynomials. We show that one of the polynomials is a special value of the bivariate Eulerian polynomial and the other…
Convolutions for Tribonacci numbers involving binomial coefficients are treated with ordinary generating functions and the diagonalization method of Hautus and Klarner. In this way, the relevant generating function can be established, which…
We describe generating functions for several important families of classical symmetric functions and shifted Schur functions. The approach is originated from vertex operator realization of symmetric functions and offers a unified method to…
We describe a method to compute the inverse Mellin transform of holonomic sequences, that is based on a method to compute the Mellin transform of holonomic functions. Both methods are implemented in the computer algebra package…
A product difference equation is proved and used for derivation by elementary methods of four combinatorial identities, eight combinatorial identities involving generalized harmonic numbers and eight combinatorial identities involving…
We introduce the concept of reflexive moment functional in two variables and the definition of reflexive orthogonal polynomial system. Also reverse matrices and their interesting algebraic properties are studied. Reverse matrices and…
In this paper, we consider linear differential equations satisfied by the generating function for Hermite polynomials and derive some new identities involving those polynomials.