O ct 2 00 1 SOME NEW FORMULAS FOR π

m at h . N T / 0 11 02 38 v 3 1 0 O ct 2 00 2 SOME NEW FORMULAS FOR π

We show how to find series expansions for π of the form π = ∞ n=0 S(n) 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.

1 5 Ju l 2 00 7 New 5 F 4 hypergeometric transformations , three - variable Mahler measures , and formulas for 1 / π Mathew

New relations are established between families of three-variable Mahler measures. Those identities are then expressed as transformations for the 5F4 hypergeometric function. We use these results to obtain two explicit 5F4 evaluations, and several new formulas for 1/π. MSC: 33C20, 33C05, 11F66

/ 05 11 06 0 v 2 1 9 O ct 2 00 6 New result on the measurement of the direct photon emission in K + → π + π 0 γ decay

A pr 2 00 7 New 5 F 4 hypergeometric transformations , three - variable Mahler measures , and formulas for 1 / π Mathew

New relations are established between families of three-variable Mahler measures. Those identities are then expressed as transformations for the 5F4 hypergeometric function. We use these results to obtain two explicit 5F4 evaluations, and several new formulas for 1/π. MSC: 33C20, 33C05, 11F66

N ov 2 00 1 SOME NEW FORMULAS FOR π

We show how to find series expansions for π of the form π = ∞ n=0 S(n) 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.