A257407 Decimal expansion of E(1/sqrt(2)) = 1.35064..., where E is the complete elliptic integral.

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, 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, 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

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

Wikipedia, Complete 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

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

Sequence in context: A100609 A104866 A165723 * A224932 A094771 A348723

Adjacent sequences: A257404 A257405 A257406 * A257408 A257409 A257410

Keyword

nonn,cons,easy

Author

Jean-François Alcover, Apr 22 2015

Status

approved