✦ LIBER ✦

Sums of Products of Bernoulli Numbers

✍ Scribed by Karl Dilcher

Publisher: Elsevier Science
Year: 1996
Tongue: English
Weight: 573 KB
Volume: 60
Category: Article
ISSN: 0022-314X
DOI: 10.1006/jnth.1996.0110

No coin nor oath required. For personal study only.

✦ Synopsis

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, and for Euler numbers and polynomials. As easy corollaries we obtain formulas for sums of products of the Riemann zeta function at even integers and of other related infinite series. 1996 Academic Press, Inc. =(n+1)(2n+1) B 2n +n \ n& 1 2+ B 2n&2 , (1.3) article no. 0110

📜 SIMILAR VOLUMES

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.

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

Computation of Euler’s type sums of the

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

✍ Aleksandar Petojević; H.M. Srivastava 📂 Article 📅 2009 🏛 Elsevier Science 🌐 English ⚖ 386 KB

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.

Faster computation of Bernoulli numbers

✍ Sandra Fillebrown 📂 Article 📅 1992 🏛 Elsevier Science 🌐 English ⚖ 689 KB

Sums of powers of complex numbers

✍ J.D Buckholtz 📂 Article 📅 1967 🏛 Elsevier Science 🌐 English ⚖ 370 KB

On the denominator of generalized Bernou

On the denominator of generalized Bernoulli numbers

✍ Albert T Lundell 📂 Article 📅 1987 🏛 Elsevier Science 🌐 English ⚖ 369 KB