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Computation of Euler’s type sums of the products of Bernoulli numbers

✍ Scribed by Aleksandar Petojević; H.M. Srivastava

Publisher
Elsevier Science
Year
2009
Tongue
English
Weight
386 KB
Volume
22
Category
Article
ISSN
0893-9659

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✦ Synopsis

In this work, the authors present several formulas which compute the following Euler's type and Dilcher's type sums of the products of Bernoulli numbers B n :

respectively, where

denotes, as usual, the multinomial coefficient.

📜 SIMILAR VOLUMES

Sums of Products of Bernoulli Numbers
Sums of Products of Bernoulli Numbers
✍ Karl Dilcher 📂 Article 📅 1996 🏛 Elsevier Science 🌐 English ⚖ 573 KB

Closed expressions are obtained for sums of products of Bernoulli numbers of the form ( 2n 2j 1 , ..., 2jN ) B 2j1 } } } B 2jN , where the summation is extended over all nonnegative integers j 1 , ..., j N with j 1 + j 2 + } } } + j N =n. Corresponding results are derived for Bernoulli polynomials,

Sums of Products of Twoq-Bernoulli Numbe
Sums of Products of Twoq-Bernoulli Numbers
✍ Junya Satoh 📂 Article 📅 1999 🏛 Elsevier Science 🌐 English ⚖ 94 KB

We extend a well-known formula for sums of products of two Bernoulli numbers to that of Carlitz's q-Bernoulli numbers. Recently Dilcher (J. Number Theory 60 (1996), 23 41) generalized the formula for sums of products of any number of Bernoulli numbers, but it is not easy to prove the generalized for

A note on sums of products of Bernoulli
A note on sums of products of Bernoulli numbers
✍ Min-Soo Kim 📂 Article 📅 2011 🏛 Elsevier Science 🌐 English ⚖ 221 KB

In this work we obtain a new approach to closed expressions for sums of products of Bernoulli numbers by using the relation of values at non-positive integers of the important representation of the multiple Hurwitz zeta function in terms of the Hurwitz zeta function.

The Frobenius problem, sums of powers of
The Frobenius problem, sums of powers of integers, and recurrences for the Bernoulli numbers
✍ Hans J.H. Tuenter 📂 Article 📅 2006 🏛 Elsevier Science 🌐 English ⚖ 139 KB

In the Frobenius problem with two variables, one is given two positive integers a and b that are relative prime, and is concerned with the set of positive numbers NR that have no representation by the linear form ax + by in nonnegative integers x and y. We give a complete characterization of the set