Abstract
We show how to find series expansions for {\small $\pi$} of the form {\small $\pi=\sum_{n=0}^\infty {S(n)}\big/{\binom{mn}{pn}a^n}$}, where {\small $S(n)$} is some polynomial in n (depending on m, p, a). We prove that there exist such expansions for {\small $m=8k$, $p=4k$, $a=(-4)^k$}, for any k, and give explicit examples for such expansions for small values of m, p, a and a.
Citation
Gert Almkvist. Christian Krattenthaler. Joakim Petersson. "Some New Formulas for 𝜋." Experiment. Math. 12 (4) 441 - 456, 2003.
Information
