Some new formulas for $π$

Details Some new formulas for $π$ Some new formulas for $π$

2001-10-22

arxiv.org/abs/math/0110238v3

Experiment. Math. 12 (2003), 441-456.

Mathematics

Number Theory

28 pages, LaTeX; some important references added

Scientific paper

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 $a$.

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