A259501 Decimal expansion of theta_3(7*i/sqrt(7)), an explicit particular value of the cubic theta function theta_3.

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

Offset

1,8

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(7*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

1.0000003618680136055734464581211946734487733839572780170205672760474...

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, A259500.

Sequence in context: A288853 A296184 A290481 * A118948 A176092 A118012

Adjacent sequences: A259498 A259499 A259500 * A259502 A259503 A259504

Keyword

nonn,cons,easy

Author

Jean-François Alcover, Jun 29 2015

Status

approved