This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A212186 #14 Jul 05 2025 19:00:23
%S A212186 3,1,0,4,3,7,9,0,1,7,8,5,5,5,5,5,0,9,8,1,8,1,7,6,9,8,6,3,1,8,7,7,9,4,
%T A212186 7,6,7,2,2,8,9,0,9,2,0,3,3,6,1,3,6,8,3,5,0,9,7,2,4,8,8,8,2,6,1,9,6,8,
%U A212186 1,4,0,3,2,6,9,9,3,9,9,9,5,8,0,2,7,8,4,6,5,6,6,3,6,1,4,8,3,9,7,6,5,8,2,8,1,1,9
%N A212186 Decimal expansion of the integral over exp(x)/sqrt(1-x^2) dx between 0 and 1.
%C A212186 This appears as the first integral in an attempt to expand exp(x) in a Chebyshev series between 0 and 1. Other integrals of the higher order terms in that expansion are generally bootstrapped from the lower order terms.
%C A212186 If we substitute x=cos(y), this is the integral over exp(cos(y)) dy from y=0 to y=Pi/2, which matches (apart from the upper limit) eq. 3.915.4 of the Gradsteyn-Ryzhik tables. - _R. J. Mathar_, Feb 15 2013
%H A212186 A. Karageorghis, <a href="http://dx.doi.org/10.1016/0377-0427(88)90396-2">A note on the Chebyshev coefficients of the general order derivative of an infinitely differentiable function</a>, J. Comp. Appl. Math 21 (1988) 129-132.
%F A212186 Equals Pi*(A197036+A197037)/2 .
%e A212186 3.104379017855555098181769863187794767228...
%t A212186 RealDigits[ Pi*(BesselI[0, 1] + StruveL[0, 1])/2, 10, 107] // First (* _Jean-François Alcover_, Feb 21 2013 *)
%t A212186 RealDigits[Integrate[Exp[x]/Sqrt[1-x^2],{x,0,1}],10,120][[1]] (* _Harvey P. Dale_, Jul 05 2025 *)
%K A212186 cons,easy,nonn
%O A212186 1,1
%A A212186 _R. J. Mathar_, Feb 13 2013