Zeilberger's Algorithm

2007 ◽  
pp. 147-158
Keyword(s):  
Zeilberger’S Algorithm ◽  
Zeilberger's Algorithm

scholarly journals On Gessel-Kaneko's identity for Bernoulli numbers

2013 ◽  
Vol 7 (1) ◽  
pp. 1-10 ◽  
Author(s):  
Hacène Belbachir ◽  
Mourad Rahmani
Keyword(s):  
Bernoulli Numbers ◽  
Umbral Calculus ◽  
Zeilberger’S Algorithm ◽  
Zeilberger's Algorithm

The present work deals with Bernoulli numbers. Using Zeilberger's algorithm, we generalize an identity on Bernoulli numbers of Gessel-Kaneko's type. Appendix written by Ira M. Gessel offers a closely related formula via umbral calculus.

scholarly journals The Abel-Zeilberger Algorithm

10.37236/2013 ◽  
2011 ◽  
Vol 18 (2) ◽  
Author(s):  
William Y.C. Chen ◽  
Qing-Hu Hou ◽  
Hai-Tao Jin
Keyword(s):  
Recurrence Relations ◽  
Difference Operators ◽  
Harmonic Numbers ◽  
Summation By Parts ◽  
Polynomial Coefficients ◽  
Zeilberger’S Algorithm ◽  
Zeilberger's Algorithm

By combining Abel's lemma on summation by parts with Zeilberger's algorithm, we give an algorithm, called the Abel-Zeilberger algorithm, to find recurrence relations for definite summations. The role of Abel's lemma can be extended to the case of linear difference operators with polynomial coefficients. This approach can be used to verify and discover identities involving harmonic numbers and derangement numbers. As examples, we use the Abel-Zeilberger algorithm to prove the Paule-Schneider identities, an identity of Andrews and Paule, and an identity of Calkin.

Sign in / Sign up

Export Citation Format

Share Document