A278146 Decimal expansion of 2^(3/2) / (sqrt(Pi)*Gamma(3/4)^2).

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

Offset: 1

Author

Wolfdieter Lang, Nov 15 2016

Keywords

• nonn
• cons

Comments

This is the value of a series of Ramanujan, namely 1 + 9*(1/4)^4 + 17*(1*5/(4*8))^4 + 25*(1*5*9/(4*8*12))^4 + ... = Sum_{k>=0} (1+8*k)*(risefac(1/4,k)/k!)^4 where risefac(x,k) = Product_{j=0..k-1} (x+j), and risefac(x,0) = 1. See the Hardy reference, p. 7, eq. (1.3) and p. 105, eq. (7.4.3) for s=1/4 (after division by s).

For the partial sums of this series see A278141/A278142.

Examples

			1.06267989991684365118249019510...
		

References

• G. H. Hardy, Ramanujan: twelve lectures on subjects suggested by his life and work, AMS Chelsea Publ., Providence, RI, 2002, pp. 7, 105.

Links

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

Crossrefs

Cf. A278141/A278142, A242439.

Programs

Mathematica

First@ RealDigits@ N[2^(3/2)/(Sqrt[Pi] Gamma[3/4]^2), 104] (* Michael De Vlieger, Nov 15 2016 *)
RealDigits[2^(3/2)/(Sqrt[Pi]*(Gamma[3/4])^2), 10, 50][[1]] (* G. C. Greubel, Jan 10 2017 *)

PARI

2^(3/2)/(sqrt(Pi)*(gamma(3/4))^2) \\ G. C. Greubel, Jan 10 2017

Formula

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

Equals 2*A242439. - Hugo Pfoertner, Apr 26 2025