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A303670
Decimal expansion of Product_{k>=1} Gamma(1 + 1/k^2).
5
7, 3, 3, 0, 2, 4, 9, 4, 3, 3, 8, 5, 8, 3, 0, 1, 6, 9, 1, 0, 9, 4, 5, 9, 9, 2, 8, 8, 4, 7, 8, 0, 9, 9, 3, 4, 9, 8, 4, 5, 3, 3, 8, 3, 5, 0, 5, 0, 0, 1, 0, 2, 2, 1, 9, 8, 2, 2, 3, 0, 0, 5, 9, 6, 1, 7, 2, 4, 1, 6, 2, 7, 2, 0, 2, 0, 5, 9, 0, 9, 6, 0, 2, 2, 2, 1, 5, 2, 0, 0, 3, 9, 5, 6, 8, 9, 2, 2, 9, 2, 7, 2, 6, 1, 2, 1
OFFSET
0,1
FORMULA
Equals Product_{k>=1} Gamma(1/k^2) / k^2.
Equals exp(-gamma*Pi^2/6 + Sum_{k>=2} (-1)^k*zeta(k)*zeta(2*k)/k), where gamma is the Euler-Mascheroni constant A001620. - Vaclav Kotesovec, Mar 09 2019
Equals exp(-gamma*Pi^2/6 + A306774).
EXAMPLE
0.73302494338583016910945992884780993498453383505001022198223...
MAPLE
Digits := 120: evalf(product(GAMMA(1+1/n^2), n = 1..infinity));
evalf(exp(-gamma*Pi^2/6 + Sum((-1)^k*Zeta(k)*Zeta(2*k)/k, k=2..infinity)), 121); # Vaclav Kotesovec, Mar 09 2019
MATHEMATICA
RealDigits[NProduct[Gamma[1 + 1/n^2], {n, 1, Infinity}, WorkingPrecision -> 120, NProductFactors -> 1000], 10, 70][[1]]
PROG
(PARI) exp(-Euler*Pi^2/6 + sumalt(k=2, (-1)^k*zeta(k)*zeta(2*k)/k)) \\ Vaclav Kotesovec, Mar 09 2019
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
Vaclav Kotesovec, Apr 28 2018
STATUS
approved