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A259498
Decimal expansion of theta_3(i/sqrt(5)), an explicit particular value of the cubic theta function theta_3.
3
1, 3, 6, 2, 6, 4, 5, 2, 3, 1, 2, 8, 7, 3, 6, 3, 3, 6, 6, 2, 8, 5, 3, 6, 2, 9, 3, 3, 7, 0, 2, 0, 4, 6, 7, 2, 3, 8, 9, 7, 9, 8, 0, 2, 4, 0, 1, 2, 2, 5, 3, 4, 8, 2, 7, 9, 9, 3, 1, 6, 1, 6, 7, 6, 8, 2, 8, 4, 7, 0, 7, 3, 9, 4, 6, 8, 2, 5, 8, 5, 3, 4, 0, 4, 8, 9, 6, 7, 8, 3, 7, 0, 1, 4, 2, 7, 2, 0, 1, 5, 4, 8, 9, 8, 3
OFFSET
1,2
LINKS
Daniel Schultz, Cubic theta functions. Adv. Math. 248, 618-697 (2013). p. 72.
Eric Weisstein's MathWorld, 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(5)) = sqrt((1/6)*(sqrt(3)-1)*(4 + sqrt(3) + 3*sqrt(5))*Gamma(1/20)*Gamma(3/20)*Gamma(7/20)*Gamma(9/20))/(4*Pi^(3/2)).
EXAMPLE
1.36264523128736336628536293370204672389798024012253482799316167682847...
MATHEMATICA
Sqrt[(1/6)*(Sqrt[3]-1)*(4 + Sqrt[3] + 3*Sqrt[5]) * Gamma[1/20] * Gamma[3/20] * Gamma[7/20] * Gamma[9/20]]/(4*Pi^(3/2)) // RealDigits[#, 10, 105]& // First
CROSSREFS
KEYWORD
nonn,cons,easy
AUTHOR
STATUS
approved