A248557 Decimal expansion of (Pi/2)^(1/4)/Gamma(3/4).

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

Offset: 0

Author

Jean-François Alcover, Dec 15 2014

Keywords

• nonn
• cons
• easy

Examples

			0.913579138156116821407242593401222089701963916393469...
		

Links

• MathOverflow, How to calculate the infinite sum of this double series?, 2014.
• Eric Weisstein's World of Mathematics, Jacobi Theta Functions.

Crossrefs

Cf. A010767, A068465, A092040, A175573, A222068, A251992.

Programs

Mathematica

RealDigits[(Pi/2)^(1/4)/Gamma[3/4], 10, 103] // First

PARI

(Pi/2)^(1/4)/gamma(3/4) \\ Michel Marcus, Dec 15 2014

Formula

Also equals theta_2(0,exp(-Pi)), where 'theta' is the elliptic theta function.

Equals A175573 / exp(4*A251992/Pi + Pi/4).

Equals Product_{k>=1} tanh(k*Pi/2). - Amiram Eldar, Jun 12 2021