cp's OEIS Frontend

A242000 Decimal expansion of delta = (1+alpha)/4, a constant appearing in Koecher's formula for Euler's gamma constant, where alpha is A065442, the Erdős-Borwein Constant.

%I A242000 #19 Feb 16 2025 08:33:22
%S A242000 6,5,1,6,7,3,7,8,8,1,0,3,8,2,2,9,4,0,9,4,5,8,2,5,3,8,0,7,9,7,7,3,1,1,
%T A242000 4,5,1,2,0,1,4,4,9,1,7,8,7,6,4,3,9,1,0,8,9,4,4,5,1,9,8,8,8,4,2,2,8,5,
%U A242000 4,6,0,5,1,8,5,8,7,1,6,7,2,6,4,1,4,2,7,9,5,0,4,1,7,5,3,8,8,9,3,9,7,4
%N A242000 Decimal expansion of delta = (1+alpha)/4, a constant appearing in Koecher's formula for Euler's gamma constant, where alpha is A065442, the Erdős-Borwein Constant.
%D A242000 Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 5.14 Digital Search Tree Constants, p. 355.
%H A242000 G. C. Greubel, <a href="/A242000/b242000.txt">Table of n, a(n) for n = 0..10000</a>
%H A242000 Steven R. Finch, <a href="http://arxiv.org/abs/2001.00578">Errata and Addenda to Mathematical Constants.</a> p. 4.
%H A242000 Eric Weisstein's Mathworld, <a href="https://mathworld.wolfram.com/Erdos-BorweinConstant.html">Erdős-Borwein Constant</a>
%F A242000 alpha = sum_{n>=1} 1/(2^n-1) = A065442 = 1.606695...
%F A242000 delta = (1+alpha)/4 = 0.65167...
%F A242000 gamma = delta - (1/2)*sum_{k>=2} (((-1)^k/((k-1)*k*(k+1)))*floor(log(k)/log(2))) = A001620 = 0.5772... (Koecher's formula).
%e A242000 0.6516737881038229409458253807977311451201449178764391089445...
%t A242000 alpha = 1/2 - QPolyGamma[0, 1, 2]/Log[2]; delta = (1+alpha)/4; RealDigits[delta, 10, 102] // First
%o A242000 (PARI) default(realprecision, 100); (1 + suminf(k=1, 1/(2^k - 1)))/4 \\ _G. C. Greubel_, Sep 06 2018
%Y A242000 Cf. A001620, A065442.
%K A242000 nonn,cons,easy
%O A242000 0,1
%A A242000 _Jean-François Alcover_, Aug 11 2014