Parametric Euler Sum Identities
نویسندگان
چکیده
We consider some parametrized classes of multiple sums first studied by Euler. Identities between meromorphic functions of one or more variables in many cases account for reduction formulae for these sums. 2005 Elsevier Inc. All rights reserved.
منابع مشابه
In Praise of an Elementary Identity of Euler
We survey the applications of an elementary identity used by Euler in one of his proofs of the Pentagonal Number Theorem. Using a suitably reformulated version of this identity that we call Euler’s Telescoping Lemma, we give alternate proofs of all the key summation theorems for terminating Hypergeometric Series and Basic Hypergeometric Series, including the terminating Binomial Theorem, the Ch...
متن کاملOn Various Combinatorial Sums and Related Identities
In this talk we give a survey of results and methods on some combinatorial sums involving binomial coefficients and related to Bernoulli and Euler polynomials. We will also talk about certain sums of minima and maxima related to Dedekind sums. Some interesting identities associated with the various sums will also be introduced. 1. A curious identity and the sum ∑ k≡r (mod m) ( n k ) In 1988 Zhi...
متن کاملIdentities Involving Two Kinds of q-Euler Polynomials and Numbers
We introduce two kinds of q-Euler polynomials and numbers, and investigate many of their interesting properties. In particular, we establish q-symmetry properties of these q-Euler polynomials, from which we recover the so-called Kaneko-Momiyama identity for the ordinary Euler polynomials, discovered recently by Wu, Sun, and Pan. Indeed, a q-symmetry and q-recurrence formulas among sum of produc...
متن کاملCOMPLETE SUM OF PRODUCTS OF (h,q)-EXTENSION OF EULER POLYNOMIALS AND NUMBERS
By using the fermionic p-adic q-Volkenborn integral, we construct generating functions of higher-order (h, q)-extension of Euler polynomials and numbers. By using these numbers and polynomials, we give new approach to the complete sums of products of (h, q)-extension of Euler polynomials and numbers one of which is given by the following form: are the multinomial coefficients and E (h) m,q (y) ...
متن کاملSymmetry Fermionic p-Adic q-Integral on ℤp for Eulerian Polynomials
Kim et al. 2012 introduced an interesting p-adic analogue of the Eulerian polynomials. They studied some identities on the Eulerian polynomials in connection with the Genocchi, Euler, and tangent numbers. In this paper, by applying the symmetry of the fermionic p-adic q-integral on Zp, defined by Kim 2008 , we show a symmetric relation between the q-extension of the alternating sum of integer p...
متن کامل