International Journal of Mathematics and Mathematical Sciences
Volume 2004 (2004), Issue 67, Pages 3653-3662
A procedure for generating infinite series identities
Naval Undersea Warfare Center Division, 1176 Howell Street, Newport 02841, RI, USA
Received 3 March 2004
Copyright © 2004 Anthony A. Ruffa. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
A procedure for generating infinite series identities makes use of the generalized method of exhaustion by analytically evaluating the inner series of the resulting double summation. Identities are generated involving both elementary and special functions. Infinite sums of special functions include those of the gamma and polygamma functions, the Hurwitz Zeta function, the polygamma function, the Gauss hypergeometric function, and the
Lerch transcendent. The procedure can be automated with Mathematica (or equivalent software).