A273087 Decimal expansion of theta_3(0, exp(-sqrt(2)*Pi)), where theta_3 is the 3rd Jacobi theta function.

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

Offset

1,3

Links

G. C. Greubel, Table of n, a(n) for n = 1..5000

Eric Weisstein's MathWorld, Jacobi Theta Functions

Wikipedia, Theta function

Formula

Equals Gamma(1/8)/(2^(9/8)*sqrt(Pi*Gamma(1/4))).

Example

1.0235239993410058634977986567249718525649146079487847418721...

Maple

evalf(GAMMA(1/8)/(2^(9/8)*sqrt(Pi*GAMMA(1/4))), 120);

Mathematica

RealDigits[EllipticTheta[3, 0, Exp[-Sqrt[2]*Pi]], 10, 105][[1]]
RealDigits[Gamma[1/8]/(2^(9/8)*Sqrt[Pi*Gamma[1/4]]), 10, 105][[1]]

Prog

(PARI) th3(x)=1 + 2*suminf(n=1, x^n^2)
th3(exp(-sqrt(2)*Pi)) \\ Charles R Greathouse IV, Jun 06 2016
(Magma) C<i> := ComplexField(); Gamma(1/8)/(2^(9/8)*Sqrt(Pi(C)*Gamma(1/4))) // G. C. Greubel, Jan 07 2018

Crossrefs

Cf. A175573, A247217, A273081, A273082, A273083, A273084, A273086.

Sequence in context: A374155 A361503 A265668 * A236434 A138182 A167835

Adjacent sequences: A273084 A273085 A273086 * A273088 A273089 A273090

Keyword

nonn,cons

Author

Vaclav Kotesovec, May 14 2016

Status

approved