OFFSET
1,2
COMMENTS
This constant is sometimes expressed as E(1/2), with a different convention of argument (Cf. Mathematica).
REFERENCES
Jonathan Borwein, David H. Bailey, Mathematics by Experiment, 2nd Edition: Plausible Reasoning in the 21st Century, CRC Press (2008), p. 145.
LINKS
G. C. Greubel, Table of n, a(n) for n = 1..10000
Eric Weisstein's World of Mathematics, Elliptic Integral of the Second Kind
FORMULA
Equals (4*B^2 + Pi)/(4*sqrt(2)*B), where B is the lemniscate constant A076390.
Equals Pi^(3/2)/Gamma(1/4)^2 + Gamma(1/4)^2/(8*Pi^(1/2)).
Equals (agm(1,sqrt(2))+Pi/agm(1,sqrt(2)))/sqrt(8) = (A053004+A062539)/A010466. - Gleb Koloskov, Jun 29 2021
EXAMPLE
1.3506438810476755025201747353387258413495223669243545453232537...
MAPLE
evalf(EllipticE(1/sqrt(2)), 120); # Vaclav Kotesovec, Apr 22 2015
MATHEMATICA
RealDigits[EllipticE[1/2], 10, 106] // First
CROSSREFS
KEYWORD
AUTHOR
Jean-François Alcover, Apr 22 2015
STATUS
approved