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Sunday, October 2, 2016

Entry 33

In a similar manner to Entry 32, given the Chudnovsky algorithm1π=12(640320)3/2k=0(6k)!(3k)!k!331631114806k+13591409(6403203)k we can use the cube root 36403203=640320 as the median,1π=12(640320+12)3/2k=0(2kk)kj=0(3)k3j(k3j)(2jj)(3jj)1631114806k+(135914098181)(64032012)k1π=12(64032012)3/2k=0(2kk)kj=03k3j(k3j)(2jj)(3jj)1631114806k+(13591409+8181)(640320+12)k where (nk) is the binomial coefficient. These are now level-9 Ramanujan-Sato series

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