In a similar manner to
Entry 32, given the Chudnovsky algorithm
1π=12(640320)3/2∞∑k=0(6k)!(3k)!k!33⋅163⋅1114806k+13591409(−6403203)k we can use the cube root
3√−6403203=−640320 as the median,
1π=12(640320+12)3/2∞∑k=0(2kk)k∑j=0(−3)k−3j(k3j)(2jj)(3jj)163⋅1114806k+(13591409−8⋅181)(−640320−12)k1π=12(640320−12)3/2∞∑k=0(2kk)k∑j=03k−3j(k3j)(2jj)(3jj)163⋅1114806k+(13591409+8⋅181)(−640320+12)k where
(nk) is the
binomial coefficient. These are now
level-9 Ramanujan-Sato series.
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