A347341 - OEIS

%I #30 Sep 27 2023 06:32:23

%S 5,7,2,4,6,7,0,3,3,4,2,4,1,1,3,2,1,8,2,3,6,2,0,7,5,8,3,3,2,3,0,1,2,5,

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

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

%N Decimal expansion of (Pi^2-3)/12.

%H Paolo Xausa, <a href="/A347341/b347341.txt">Table of n, a(n) for n = 0..10000</a>

%H M. I. Shamos, <a href="http://euro.ecom.cmu.edu/people/faculty/mshamos/cat.pdf">A Catalog of the Real Numbers</a>, p. iii.

%H <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>

%F Equals (Pi^2-3)/12 = A126561 + 1/2 = A072691 - 1/4.

%F Equals Sum_{k=1..infinity} (-1)^(k+1)*cos(k)/k^2.

%e 0.57246703342411321823620758332301259460947495060...

%t RealDigits[(Pi^2-3)/12,10,120][[1]] (* _Harvey P. Dale_, Jun 06 2022 *)

%o (PARI) sumalt(k=1,(-1)^(k+1)*cos(k)/k^2) \\ _Hugo Pfoertner_, Aug 27 2021

%Y Cf. A000796.

%Y Almost the same as A072691, A126561.

%K nonn,cons

%O 0,1

%A _Paolo Xausa_, Aug 27 2021