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A273082
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Decimal expansion of theta_3(0, exp(-4*Pi)), where theta_3 is the 3rd Jacobi theta function.
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8
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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
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OFFSET
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1,7
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LINKS
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FORMULA
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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)).
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EXAMPLE
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1.00000697468471241799127935745572277338608481181934395967...
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MAPLE
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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);
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MATHEMATICA
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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]]
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PROG
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(Magma) C<i> := ComplexField(); ((2+2^(3/4))/4)*Pi(C)^(1/4)/Gamma(3/4) // G. C. Greubel, Jan 07 2018
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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