A363684 Decimal expansion of Product_{k>=1} Gamma(2k/(2k-1)) / Gamma(1+1/(2k)).

1, 0, 6, 2, 1, 5, 0, 9, 0, 5, 5, 7, 1, 0, 5, 7, 2, 8, 0, 6, 9, 6, 8, 3, 7, 3, 6, 2, 9, 3, 8, 0, 9, 9, 9, 0, 4, 2, 5, 2, 0, 7, 9, 5, 5, 2, 0, 0, 4, 5, 6, 9, 3, 3, 3, 4, 0, 7, 9, 8, 7, 0, 0, 9, 0, 5, 3, 7, 9, 8, 9, 3, 7, 0, 7, 7, 1, 4, 0, 8, 2, 9, 1, 9, 3, 6, 1, 8, 2, 5, 3, 6, 8, 6, 6, 9, 3, 1, 7, 7, 6, 0, 2, 1, 9, 7

Offset: 1

Author

R. J. Mathar, Jun 15 2023

Keywords

• cons
• nonn

Examples

			1.06215090557105728069683736293...
		

Links

• Henri Cohen, Fernando Rodriguez Villegas, and Don Zagier, Convergence Acceleration of Alternating Series, Exp. Math. 9 (1) (2000) 3-12.
• Vaclav Kotesovec, Why do I get different results for the products of two identical expressions ?, Mathematica Stack Exchange, Jun 10 2024.

Crossrefs

Cf. A303670.

Programs

Maple

evalf(Product(2*k*GAMMA(1/(2*k - 1))/((2*k - 1)*GAMMA(1/(2*k))), k = 1..infinity), 120); # Vaclav Kotesovec, Jun 10 2024

PARI

default(realprecision, 200); exp(sumpos(k=1, log(2*k) + log(gamma(1/(2*k-1))) - log(2*k-1) - log(gamma(1/(2*k))) )) \\ Vaclav Kotesovec, Jun 10 2024

Extensions

More terms from Vaclav Kotesovec, Jun 10 2024