Multisection method for Apéry-like series

Abstract

Applying the multisection series method to the MacLaurin series expansion of arcsin-function, we transform the Apéry–like series involving the central binomial coefficients into systems of linear equations. By resolving the  linear systems (for example, by Mathematica), we establish numerous remarkable infinite series formulae for π and logarithm functions, including several recent results due to Almkvist et al. (2003) and Zheng (2008).