A358450 Decimal expansion of 2*EllipticK(i) - EllipticE(i), reciprocal of A088375.

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

Offset

0,1

Links

Table of n, a(n) for n=0..85.

Formula

Equals (a/b - b/a)*b^(1/2), where a = sqrt(2)*Gamma(5/4)^2 and b = Pi/4.

Equals sqrt(2) * (EllipticK(sqrt(2)/2) - EllipticE(sqrt(2)/2)).

Equals Integral_{x=0..Pi/2} cos(x)^2 / sqrt(1 + sin(x)^2).

Example

0.7119586597782638015124585488053977677277711441...

Maple

Digits := 100: a := sqrt(2)*GAMMA(5/4)^2: b := Pi/4: evalf((a/b - b/a)*b^(1/2), Digits)*10^90: ListTools:-Reverse(convert(floor(%), base, 10));

Mathematica

With[{a = Sqrt[2]*Gamma[5/4]^2, b = Pi/4}, RealDigits[(a/b - b/a)*b^(1/2), 10, 120][[1]]] (* Amiram Eldar, Nov 19 2022 *)

Crossrefs

Cf. A088375.

Sequence in context: A305607 A229779 A050179 * A183352 A217510 A273506

Adjacent sequences: A358447 A358448 A358449 * A358451 A358452 A358453

Keyword

nonn,cons

Author

Peter Luschny, Nov 19 2022

Status

approved