Some New Formulas for π

Abstract

We show how to find series expansions for π of the form π = Σ^∞ _{n =0} S(n)/ a_n , where S(n) is some polynomial in n (depending on m, p, a). We prove that there exist such expansions for m = 8k, p = 4k, a = (−4)k, for any k, and give explicit examples for such expansions for small values of m, p, and a.