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Revision History for A273083

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A273083

Decimal expansion of theta_3(0, exp(-5*Pi)), where theta_3 is the 3rd Jacobi theta function.
(history; published version)

#11 by Charles R Greathouse IV at Thu Sep 08 08:46:16 EDT 2022

PROG

(MAGMAMagma) C<i> := ComplexField(); Sqrt(2/5 + 1/Sqrt(5))*Pi(C)^(1/4)/Gamma(3/4) // G. C. Greubel, Jan 07 2018

Discussion

Thu Sep 08

08:46

OEIS Server: https://oeis.org/edit/global/2944

#10 by N. J. A. Sloane at Sun Jan 07 23:55:52 EST 2018

STATUS

proposed

approved

#9 by G. C. Greubel at Sun Jan 07 23:06:46 EST 2018

STATUS

editing

proposed

#8 by G. C. Greubel at Sun Jan 07 23:06:29 EST 2018

LINKS

G. C. Greubel, <a href="/A273083/b273083.txt">Table of n, a(n) for n = 1..10000</a>

FORMULA

Equals sqrt(2/5 + 1/sqrt(5)) * Pi^(1/4)/Gamma(3/4).

PROG

(MAGMA) C<i> := ComplexField(); Sqrt(2/5 + 1/Sqrt(5))*Pi(C)^(1/4)/Gamma(3/4) // G. C. Greubel, Jan 07 2018

STATUS

approved

editing

#7 by Charles R Greathouse IV at Mon Jun 06 02:15:44 EDT 2016

STATUS

editing

approved

#6 by Charles R Greathouse IV at Mon Jun 06 02:15:42 EDT 2016

PROG

(PARI) th3(x)=1 + 2*suminf(n=1, x^n^2)

th3(exp(-5*Pi)) \\ Charles R Greathouse IV, Jun 06 2016

STATUS

approved

editing

#5 by Vaclav Kotesovec at Sat May 14 18:24:58 EDT 2016

STATUS

editing

approved

#4 by Vaclav Kotesovec at Sat May 14 18:14:25 EDT 2016

FORMULA

sqrt(2/5 + 1/sqrt(5)) * Pi^(1/4)/Gamma(3/4).

MAPLE

evalf(sqrt(2/5 + 1/sqrt(5)) * Pi^(1/4)/GAMMA(3/4), 120);

MATHEMATICA

RealDigits[Sqrt[2/5 + 1/Sqrt[5]] * Pi^(1/4)/Gamma[3/4], 10, 105][[1]]

#3 by Vaclav Kotesovec at Sat May 14 18:11:29 EDT 2016

EXAMPLE

1.0000003014034550780129221506549039080802236178954948667347...

#2 by Vaclav Kotesovec at Sat May 14 17:50:41 EDT 2016

NAME

allocated for Vaclav KotesovecDecimal expansion of theta_3(0, exp(-5*Pi)), where theta_3 is the 3rd Jacobi theta function.

DATA

1, 0, 0, 0, 0, 0, 0, 3, 0, 1, 4, 0, 3, 4, 5, 5, 0, 7, 8, 0, 1, 2, 9, 2, 2, 1, 5, 0, 6, 5, 4, 9, 0, 3, 9, 0, 8, 0, 8, 0, 2, 2, 3, 6, 1, 7, 8, 9, 5, 4, 9, 4, 8, 6, 6, 7, 3, 4, 7, 7, 7, 4, 3, 7, 4, 8, 7, 6, 2, 8, 2, 1, 3, 3, 1, 0, 3, 1, 5, 1, 3, 9, 6, 2, 7, 4, 2, 8, 0, 5, 8, 1, 4, 3, 4, 4, 2, 8, 4, 2, 9, 8, 5, 5, 9

OFFSET

1,8

LINKS

Wikipedia, <a href="http://en.wikipedia.org/wiki/Theta_function#Explicit_values">Theta function</a>

MATHEMATICA

RealDigits[EllipticTheta[3, 0, Exp[-5*Pi]], 10, 105][[1]]

CROSSREFS

Cf. A175573, A247217, A273081, A273082, A273084.

KEYWORD

allocated

nonn,cons

AUTHOR

Vaclav Kotesovec, May 14 2016

STATUS

approved

editing