

A257407


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


1



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
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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)).


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. A076390, A093341, A105419.
Sequence in context: A100609 A104866 A165723 * A224932 A094771 A245673
Adjacent sequences: A257404 A257405 A257406 * A257408 A257409 A257410


KEYWORD

nonn,cons,easy


AUTHOR

JeanFrançois Alcover, Apr 22 2015


STATUS

approved



