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

Author

Peter Luschny, Nov 19 2022

Keywords

• nonn
• cons

Examples

			0.7119586597782638015124585488053977677277711441...
		

Crossrefs

Cf. A088375.

Programs

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 *)

PARI

2*ellK(I) - ellE(I) \\ Charles R Greathouse IV, Feb 04 2025

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).