A259500 Decimal expansion of theta_3(i/sqrt(7)), an explicit particular value of the cubic theta function theta_3.

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

Offset

1,2

Links

Table of n, a(n) for n=1..105.

Daniel Schultz, Cubic theta functions. Adv. Math. 248, 618-697 (2013). p. 72.

Eric Weisstein's MathWorld, Dedekind Eta Function

Wikipedia, Dedekind eta function

Formula

theta_3(tau) = eta(tau/3)^3 + 3*eta(3*tau)^3)/eta(tau), where 'eta' is the Dedekind eta modular elliptic function.

theta_3(i/sqrt(7)) = (sqrt((1/2)*(5 + sqrt(21))*sqrt((1/2)*(sqrt(3) + sqrt(7))) - 3^(7/4)/2)*Gamma(1/7)*Gamma(2/7)*Gamma(4/7))/((2^(5/2)*3^(1/8)*7^(-1/4)*Pi^2)).

Example

1.56346809432790055204995892408930094067512600187674126972416533519...

Mathematica

(Sqrt[(1/2)*(5 + Sqrt[21])*Sqrt[(1/2)*(Sqrt[3] + Sqrt[7])] - 3^(7/4)/2] * Gamma[1/7] * Gamma[2/7] * Gamma[4/7])/((2^(5/2)*3^(1/8)*7^(-1/4)*Pi^2)) // RealDigits[#, 10, 105]& // First

Crossrefs

Cf. A259498, A259499, A259501.

Sequence in context: A060296 A114598 A272489 * A274082 A199666 A307619

Adjacent sequences: A259497 A259498 A259499 * A259501 A259502 A259503

Keyword

nonn,cons,easy

Author

Jean-François Alcover, Jun 29 2015

Status

approved