Some New Formulas for 𝜋
Almkvist, Gert ; Krattenthaler, Christian ; Petersson, Joakim
Experiment. Math., Tome 12 (2003) no. 1, p. 441-456 / Harvested from Project Euclid
Text on Project Euclid
PDF
Alt PDF
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.
Publié le : 2003-05-14
Classification:  Fast converging series for Pi,  determinant evaluations,  11Y60,  15A15 
@article{1087568020,
     author = {Almkvist, Gert and Krattenthaler, Christian and Petersson, Joakim},
     title = {Some New Formulas for },
     journal = {Experiment. Math.},
     volume = {12},
     number = {1},
     year = {2003},
     pages = { 441-456},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1087568020}
}

Almkvist, Gert; Krattenthaler, Christian; Petersson, Joakim. Some New Formulas for 𝜋. Experiment. Math., Tome 12 (2003) no. 1, pp.  441-456. http://gdmltest.u-ga.fr/item/1087568020/