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A273082 Decimal expansion of theta_3(0, exp(-4*Pi)), where theta_3 is the 3rd Jacobi theta function. 8
1, 0, 0, 0, 0, 0, 6, 9, 7, 4, 6, 8, 4, 7, 1, 2, 4, 1, 7, 9, 9, 1, 2, 7, 9, 3, 5, 7, 4, 5, 5, 7, 2, 2, 7, 7, 3, 3, 8, 6, 0, 8, 4, 8, 1, 1, 8, 1, 9, 3, 4, 3, 9, 5, 9, 6, 7, 0, 2, 4, 3, 4, 2, 3, 6, 2, 3, 8, 8, 2, 3, 7, 0, 8, 1, 9, 5, 5, 9, 4, 5, 4, 9, 6, 1, 9, 2, 5, 3, 0, 0, 9, 2, 4, 6, 2, 9, 9, 5, 1, 4, 6, 7, 9, 7 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET
1,7
LINKS
Wikipedia, Theta function
FORMULA
Equals (2 + 2^(3/4))/4 * Pi^(1/4) / Gamma(3/4).
Equals (1 + 2^(1/4)) * Gamma(1/4) / (2^(7/4)*Pi^(3/4)).
Equals sqrt((A247217^2 + A259149^4/A259150^2)/2). - Vaclav Kotesovec, May 17 2023
EXAMPLE
1.00000697468471241799127935745572277338608481181934395967...
MAPLE
evalf((2+2^(3/4))/4*Pi^(1/4)/GAMMA(3/4), 120);
evalf((1 + 2^(1/4)) * GAMMA(1/4) / (2^(7/4)*Pi^(3/4)), 120);
MATHEMATICA
RealDigits[EllipticTheta[3, 0, Exp[-4*Pi]], 10, 105][[1]]
RealDigits[(2 + 2^(3/4))/4 * Pi^(1/4) / Gamma[3/4], 10, 105][[1]]
RealDigits[(1 + 2^(1/4)) * Gamma[1/4] / (2^(7/4)*Pi^(3/4)), 10, 105][[1]]
PROG
(PARI) (2^.25+1)*gamma(1/4)/sqrtn(128*Pi^3, 4) \\ Charles R Greathouse IV, Jun 06 2016
(Magma) C<i> := ComplexField(); ((2+2^(3/4))/4)*Pi(C)^(1/4)/Gamma(3/4) // G. C. Greubel, Jan 07 2018
CROSSREFS
Sequence in context: A229921 A145429 A194789 * A065414 A198135 A019813
KEYWORD
nonn,cons
AUTHOR
Vaclav Kotesovec, May 14 2016
STATUS
approved

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Last modified March 29 08:13 EDT 2024. Contains 371265 sequences. (Running on oeis4.)