A259499 Decimal expansion of theta_3(5*i/sqrt(5)), an explicit particular value of the cubic theta function theta_3.

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

Offset

1,7

Links

Table of n, a(n) for n=1..104.

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(5*i/sqrt(5)) = sqrt((1/30)*(1 + 3*sqrt(3) + 3*(sqrt(5) + sqrt(15)))*Gamma(1/20)*Gamma(3/20)*Gamma(7/20)*Gamma(9/20))/(4*Pi^(3/2)).

Example

1.00000474760635187188637766879472447144246277056540611713536529453...

Mathematica

Sqrt[(1/30)*(1 + 3*Sqrt[3] + 3*(Sqrt[5] + Sqrt[15])) * Gamma[1/20] * Gamma[3/20] * Gamma[7/20] * Gamma[9/20]]/(4*Pi^(3/2)) // RealDigits[#, 10, 104]& // First

Prog

(PARI) sqrt((1/30)*(1 + 3*sqrt(3) + 3*(sqrt(5) + sqrt(15)))*gamma(1/20)*gamma(3/20)*gamma(7/20)*gamma(9/20))/(4*Pi^(3/2)) \\ Michel Marcus, Jun 29 2015

Crossrefs

Cf. A259498, A259500, A259501.

Sequence in context: A106739 A112677 A010712 * A254398 A081884 A059143

Adjacent sequences: A259496 A259497 A259498 * A259500 A259501 A259502

Keyword

nonn,cons,easy

Author

Jean-François Alcover, Jun 29 2015

Status

approved