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 A247217 Decimal expansion of theta_3(0, exp(-2*Pi)), where theta_3 is the 3rd Jacobi theta function. 8
 1, 0, 0, 3, 7, 3, 4, 8, 8, 5, 4, 8, 7, 7, 3, 9, 0, 9, 1, 0, 4, 7, 6, 7, 9, 5, 9, 5, 0, 6, 6, 9, 5, 3, 8, 6, 6, 2, 0, 7, 9, 9, 4, 3, 3, 2, 4, 4, 4, 5, 1, 9, 4, 0, 8, 2, 5, 4, 9, 5, 8, 1, 5, 3, 2, 4, 7, 3, 2, 5, 1, 7, 3, 3, 2, 9, 5, 6, 3, 7, 9, 8, 0, 5, 6, 9, 4, 9, 8, 3, 2, 1, 6, 6, 4, 4, 4, 2, 3, 5, 2, 7 (list; constant; graph; refs; listen; history; text; internal format)
 OFFSET 1,4 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 (4*Pi*sqrt(2) + 6*Pi)^(1/4)/(2*Gamma(3/4)). Equals Sum_{n=-infinity..infinity} exp(-2*Pi*n^2). EXAMPLE 1.0037348854877390910476795950669538662079943324445194... MATHEMATICA RealDigits[(4*Pi*Sqrt[2] + 6*Pi)^(1/4)/(2*Gamma[3/4]), 10, 102] // First PROG (PARI) (4*Pi*sqrt(2) + 6*Pi)^(1/4)/(2*gamma(3/4)) \\ Michel Marcus, Nov 26 2014 (Magma) C := ComplexField(); (4*Pi(C)*Sqrt(2) + 6*Pi(C))^(1/4)/(2*Gamma(3/4)) // G. C. Greubel, Jan 07 2018 CROSSREFS Cf. A000122, A175573 (theta_3(0, exp(-Pi)), A273081, A273082, A273083, A273084. Cf. A273087, A273086. Sequence in context: A195769 A021968 A132821 * A252734 A101636 A193534 Adjacent sequences: A247214 A247215 A247216 * A247218 A247219 A247220 KEYWORD nonn,cons,easy AUTHOR Jean-François Alcover, Nov 26 2014 STATUS approved

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Last modified August 4 16:31 EDT 2024. Contains 374923 sequences. (Running on oeis4.)