Infinite families of accelerated series for some classical constants by the Markov-WZ Method

A function H(x,z), in the integer variables x and z, is called hypergeometric if H(x+1,z)/H(x,z) and H(x,z+1)/H(x,z) are rational functions of x and z. In this article we consider only those hypergeometric functions which are a ratio of products of factorials (we call such hypergeometric functions purehypergeometric). A P-recursive function is a function that satisfies a linear recurrence relation with polynomial coefficients. A pair (H,G) is called a Markov-WZ pair (MWZ-pair for short) if there exists a polynomial P(x,z) in z of the form P(x,z) = a0(x)+a1(x)z+ · · ·+aL(x)z, (POLY)