The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A273086 Decimal expansion of theta_3(0, exp(-sqrt(6)*Pi)), where theta_3 is the 3rd Jacobi theta function. 5
 1, 0, 0, 0, 9, 0, 9, 9, 2, 1, 8, 8, 7, 2, 5, 6, 7, 6, 2, 9, 1, 9, 2, 8, 6, 0, 0, 4, 1, 2, 1, 5, 6, 6, 6, 7, 1, 8, 0, 4, 5, 8, 8, 1, 4, 6, 7, 3, 0, 3, 0, 1, 3, 3, 0, 8, 5, 9, 2, 4, 1, 7, 9, 6, 8, 1, 3, 9, 5, 8, 5, 4, 2, 0, 8, 7, 9, 5, 0, 0, 5, 6, 3, 3, 2, 7, 5, 4, 2, 2, 0, 2, 2, 1, 8, 2, 9, 1, 1, 4, 7, 4, 2, 1, 8 (list; constant; graph; refs; listen; history; text; internal format)
 OFFSET 1,5 LINKS G. C. Greubel, Table of n, a(n) for n = 1..10000 Eric Weisstein's MathWorld, Jacobi Theta Functions Wikipedia, Theta function FORMULA Equals ((6 + sqrt(6*(3 + 2*sqrt(2)))) * Gamma(1/24) * Gamma(5/24) * Gamma(7/24) * Gamma(11/24))^(1/4) / (2*6^(3/8)*Pi^(3/4)). Equals (4 - sqrt(2) + sqrt(6))^(1/4) * sqrt(Gamma(1/24)*Gamma(11/24)) / (2^(3/2)*3^(3/8)*Pi^(3/4)). EXAMPLE 1.0009099218872567629192860041215666718045881467303013308592... MAPLE evalf(((6 + sqrt(6*(3 + 2*sqrt(2)))) * GAMMA(1/24) * GAMMA(5/24) * GAMMA(7/24) * GAMMA(11/24))^(1/4) / (2*6^(3/8)*Pi^(3/4)), 120); evalf((4 - sqrt(2) + sqrt(6))^(1/4) * sqrt(GAMMA(1/24)*GAMMA(11/24)) / (2^(3/2)*3^(3/8)*Pi^(3/4)), 120); MATHEMATICA RealDigits[EllipticTheta[3, 0, Exp[-Sqrt[6]*Pi]], 10, 105][[1]] RealDigits[((6 + Sqrt[6*(3 + 2*Sqrt[2])]) * Gamma[1/24] * Gamma[5/24] * Gamma[7/24] * Gamma[11/24])^(1/4) / (2*6^(3/8)*Pi^(3/4)), 10, 105][[1]] RealDigits[(4 - Sqrt[2] + Sqrt[6])^(1/4) * Sqrt[Gamma[1/24]*Gamma[11/24]] / (2^(3/2)*3^(3/8)*Pi^(3/4)), 10, 105][[1]] PROG (PARI) th3(x)=1 + 2*suminf(n=1, x^n^2) th3(exp(-sqrt(6)*Pi)) \\ Charles R Greathouse IV, Jun 06 2016 CROSSREFS Cf. A175573, A247217, A273081, A273082, A273083, A273084, A086231, A273087. Sequence in context: A176523 A242400 A197264 * A332093 A056965 A347688 Adjacent sequences:  A273083 A273084 A273085 * A273087 A273088 A273089 KEYWORD nonn,cons AUTHOR Vaclav Kotesovec, May 14 2016 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified September 28 10:48 EDT 2021. Contains 347714 sequences. (Running on oeis4.)