A242822 - OEIS

%I #23 Nov 22 2024 07:38:08

%S 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,

%T 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,

%U 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

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

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

%H G. C. Greubel, <a href="/A242822/b242822.txt">Table of n, a(n) for n = 1..10000</a>

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

%F Equals Product_{k>=1} (1 + 1/A002145(k)^2)/(1 - 1/A002145(k)^2) = A243381 / A243379. - _Vaclav Kotesovec_, Apr 30 2020

%F Equals Sum_{q in A004614} 2^A001221(q)/q^2. - _R. J. Mathar_, Jan 27 2021

%F Equals 1/A377753. - _Hugo Pfoertner_, Nov 22 2024

%e 1.3468852519994065951820075554411...

%p s:= convert(evalf(Pi^2/(8*Catalan), 140), string):

%p map(parse, subs("."=NULL, [seq(i, i=s)]))[]; # _Alois P. Heinz_, May 23 2014

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

%o (PARI) default(realprecision, 100); Pi^2/(8*Catalan) \\ _G. C. Greubel_, Aug 25 2018

%o (Magma) SetDefaultRealField(RealField(100)); R:=RealField(); Pi(R)^2/(8*Catalan(R)); // _G. C. Greubel_, Aug 25 2018

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

%K nonn,cons

%O 1,2

%A _Jean-François Alcover_, May 23 2014