A242822 Decimal expansion of B. Davis' constant Pi^2/(8*G), a Riesz-Kolmogorov constant, where G is Catalan's constant.

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

Offset: 1

Author

Jean-François Alcover, May 23 2014

Keywords

• nonn
• cons

Examples

			1.3468852519994065951820075554411...
		

References

• Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 7.7 Riesz-Kolmogorov Constants, p. 474.

Links

• G. C. Greubel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A001221, A002145, A004614, A006752, A111003, A330890, A377753.

Programs

Magma

SetDefaultRealField(RealField(100)); R:=RealField(); Pi(R)^2/(8*Catalan(R)); // G. C. Greubel, Aug 25 2018

Maple

s:= convert(evalf(Pi^2/(8*Catalan), 140), string):
map(parse, subs("."=NULL, [seq(i, i=s)]))[]; # Alois P. Heinz, May 23 2014

Mathematica

RealDigits[Pi^2/(8*Catalan), 10, 100] // First

PARI

default(realprecision, 100); Pi^2/(8*Catalan) \\ G. C. Greubel, Aug 25 2018

Formula

(Sum_{n>=0} 1/(2*n + 1)^2) / (Sum_{n>=0} (-1)^n/(2*n + 1)^2) = A111003/A006752.

Equals Product_{k>=1} (1 + 1/A002145(k)^2)/(1 - 1/A002145(k)^2) = A243381 / A243379. - Vaclav Kotesovec, Apr 30 2020

Equals Sum_{q in A004614} 2^A001221(q)/q^2. - R. J. Mathar, Jan 27 2021

Equals 1/A377753. - Hugo Pfoertner, Nov 22 2024