[seqfan] A series for exp(Pi)

Jaume Oliver i Lafont joliverlafont at gmail.com
Sun Oct 25 11:10:59 CET 2009

Thank you very much, Simon, Alexander and Richard.

After decomposing into even and odd parts and grouping common factors,
these one-line steps compute the sequence on PARI:

gp > G(n)=gamma(n)
gp > even(n)=(1+(-1)^n)/G(3*I)/G(-3*I)
gp > odd(n)=3*(1-(-1)^n)/G(1/2+3*I)/G(1/2-3*I)
gp > a(n)=2^(n-1)*G(n/2+3*I)*G(n/2-3*I)*(even(n)+odd(n))

Six gamma functions with different argument appear. Is there a simpler solution?


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