Apéry limits and special values of L-functions

We describe a general method to determine the Apéry limits of a differential equation that has a modular-function origin. As a by-product of our analysis, we discover a family of identities involving the special values of L-functions associated with modular forms. The proof of these identities is independent of differential equations and Apéry limits. © 2008 Elsevier Inc. All rights reserved