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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
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.
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
nonn,cons,easy
AUTHOR
STATUS
approved