A247217 Decimal expansion of theta_3(0, exp(-2*Pi)), where theta_3 is the 3rd Jacobi theta function.

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

Offset: 1

Author

Jean-François Alcover, Nov 26 2014

Keywords

• nonn
• cons
• easy

Examples

			1.0037348854877390910476795950669538662079943324445194...
		

Links

• G. C. Greubel, Table of n, a(n) for n = 1..10000
• Eric Weisstein's MathWorld, Jacobi Theta Functions
• Wikipedia, Theta function

Crossrefs

Cf. A000122, A175573 (theta_3(0, exp(-Pi))), A273081, A273082, A273083, A273084.

Cf. A273087, A273086.

Programs

Magma

C := ComplexField(); (4*Pi(C)*Sqrt(2) + 6*Pi(C))^(1/4)/(2*Gamma(3/4)); // G. C. Greubel, Jan 07 2018

Mathematica

RealDigits[(4*Pi*Sqrt[2] + 6*Pi)^(1/4)/(2*Gamma[3/4]), 10, 102] // First

PARI

(4*Pi*sqrt(2) + 6*Pi)^(1/4)/(2*gamma(3/4)) \\ Michel Marcus, Nov 26 2014

Formula

Equals (4*Pi*sqrt(2) + 6*Pi)^(1/4)/(2*Gamma(3/4)).

Equals Sum_{n=-infinity..infinity} exp(-2*Pi*n^2).