A175573 Decimal expansion of Pi^(1/4)/Gamma(3/4).

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

Offset

1,3

Comments

Entry 34 a of chapter 11 of Ramanujan's second notebook. Entry 34 b is A085565.

Links

G. C. Greubel, Table of n, a(n) for n = 1..5000

Bruce C. Berndt, Chapter 11 of Ramanujan's second notebook, Bull. Lond. Math. Soc., Vol. 15, No. 4 (1983), 273-320.

Wikipedia, Theta function.

Formula

Equals A092040 / A068465.

Equals Sum_{n=-oo..oo} exp(-Pi*n^2), or also EllipticTheta(3, 0, exp(-Pi)). - Jean-François Alcover, Jul 04 2013

Equals sqrt(A175574). - Amiram Eldar, Jul 04 2023

Equals Gamma(1/4)/(sqrt(2)*Pi^(3/4)). - Vaclav Kotesovec, Jul 04 2023

Equals Product_{k>=1} tanh((1/2 + i/2)*Pi*k), i=sqrt(-1). - _Antonio Graciá Llorente, Mar 20 2024

Equals Product_{k>=0} (1/2)*(((k+1/2)/(k+1))^(1/2)+((k+1)/(k+1/2))^(1/2)). - Antonio Graciá Llorente, Jul 23 2024

Example

1.0864348112133080145753161...

Maple

Pi^(1/4)/GAMMA(3/4) ; evalf(%) ;

Mathematica

RealDigits[ Pi^(1/4)/Gamma[3/4], 10, 105][[1]] (* Jean-François Alcover, Jul 04 2013 *)

Prog

(PARI) Pi^(1/4)/gamma(3/4) \\ G. C. Greubel, Nov 05 2017
(PARI) 2*suminf(k=0, exp(-Pi)^(k^2))-1 \\ Hugo Pfoertner, Sep 17 2018
(Magma) C<i> := ComplexField(); [(Pi(C))^(1/4)/Gamma(3/4)]; // G. C. Greubel, Nov 05 2017

Crossrefs

Cf. A175574, A247217, A273081, A273082, A273083, A273084.

Sequence in context: A059631 A333198 A093019 * A296494 A261027 A296041

Adjacent sequences: A175570 A175571 A175572 * A175574 A175575 A175576

Keyword

cons,easy,nonn

Author

R. J. Mathar, Jul 15 2010

Status

approved