A303670 Decimal expansion of Product_{k>=1} Gamma(1 + 1/k^2).

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

Links

Table of n, a(n) for n=0..105.

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

Cf. A306769, A306774, A324590.

Sequence in context: A245532 A324714 A075564 * A135041 A021581 A265411

Adjacent sequences: A303667 A303668 A303669 * A303671 A303672 A303673

Keyword

nonn,cons

Author

Vaclav Kotesovec, Apr 28 2018

Status

approved