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

1,4

Links

G. C. Greubel, Table of n, a(n) for n = 1..10000

Eric Weisstein's MathWorld, Jacobi Theta Functions

Wikipedia, Theta function

Formula

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

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

Example

1.0037348854877390910476795950669538662079943324445194...

Mathematica

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

Prog

(PARI) (4*Pi*sqrt(2) + 6*Pi)^(1/4)/(2*gamma(3/4)) \\ Michel Marcus, Nov 26 2014
(Magma) C<i> := ComplexField(); (4*Pi(C)*Sqrt(2) + 6*Pi(C))^(1/4)/(2*Gamma(3/4)) // G. C. Greubel, Jan 07 2018

Crossrefs

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

Cf. A273087, A273086.

Sequence in context: A195769 A021968 A132821 * A252734 A101636 A193534

Adjacent sequences: A247214 A247215 A247216 * A247218 A247219 A247220

Keyword

nonn,cons,easy

Author

Jean-François Alcover, Nov 26 2014

Status

approved