A257407 - OEIS

%I #28 Jul 01 2021 16:42:20

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

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

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

%N Decimal expansion of E(1/sqrt(2)) = 1.35064..., where E is the complete elliptic integral.

%C This constant is sometimes expressed as E(1/2), with a different convention of argument (Cf. Mathematica).

%D Jonathan Borwein, David H. Bailey, Mathematics by Experiment, 2nd Edition: Plausible Reasoning in the 21st Century, CRC Press (2008), p. 145.

%H G. C. Greubel, <a href="/A257407/b257407.txt">Table of n, a(n) for n = 1..10000</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/EllipticIntegraloftheSecondKind.html">Elliptic Integral of the Second Kind</a>

%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Elliptic_integral#Complete_elliptic_integral_of_the_second_kind">Complete elliptic integral of the second kind</a>

%F Equals (4*B^2 + Pi)/(4*sqrt(2)*B), where B is the lemniscate constant A076390.

%F Equals Pi^(3/2)/Gamma(1/4)^2 + Gamma(1/4)^2/(8*Pi^(1/2)).

%F Equals (agm(1,sqrt(2))+Pi/agm(1,sqrt(2)))/sqrt(8) = (A053004+A062539)/A010466. - _Gleb Koloskov_, Jun 29 2021

%e 1.3506438810476755025201747353387258413495223669243545453232537...

%p evalf(EllipticE(1/sqrt(2)),120); # _Vaclav Kotesovec_, Apr 22 2015

%t RealDigits[EllipticE[1/2], 10, 106] // First

%Y Cf. A010466, A053004, A062539, A076390, A093341, A105419.

%K nonn,cons,easy

%O 1,2

%A _Jean-François Alcover_, Apr 22 2015