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A247217 Decimal expansion of theta_3(0, exp(-2*Pi)), where theta_3 is the 3rd Jacobi theta function. 8
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 (list; constant; graph; refs; listen; history; text; internal format)
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-Fran├žois Alcover, Nov 26 2014

STATUS

approved

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Last modified July 25 16:39 EDT 2021. Contains 346291 sequences. (Running on oeis4.)