Can I read Some New Formulas for $\Pi$ on EtoBox?

Some New Formulas for $\Pi$ by Almkvist, Gert; Krattenthaler, Christian; Petersson, Joakim is a scholarly article available to read on EtoBox.

What is Some New Formulas for $\Pi$ about?

We show how to find series expansions for $\pi$ of the form $\pi=\sum_{n=0}^\infty {S(n)}\big/{\binom{mn}{pn}a^n}$, 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 $a$.

Author

Almkvist, Gert; Krattenthaler, Christian; Petersson, Joakim

Published

2001

Language

EN