A249282 Decimal expansion of K(1/4), where K is the complete elliptic integral of the first kind.

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

Offset

1,2

Links

Table of n, a(n) for n=1..102.

Steven R. Finch, Gergonne-Schwarz Surface, April 12, 2013. [Cached copy, with permission of the author]

Eric Weisstein's World of Mathematics, Complete Elliptic Integral of the First Kind

Formula

From Paul D. Hanna, Mar 25 2024: (Start)

K(1/4) = Pi/2 * Sum_{n>=0} binomial(2*n,n)^2/16^n * (1/4)^n.

K(1/4) = Pi/2 * sqrt( Sum_{n>=0} binomial(2*n,n)^3/16^n * (m*(1-m))^n ), where m = 1/4. (End)

Example

1.685750354812596042871203657799076989500800894141089...

Maple

evalf(EllipticK(1/2), 120); # Vaclav Kotesovec, Apr 22 2015

Mathematica

RealDigits[EllipticK[1/4], 10, 102] // First

Crossrefs

Cf. A093341 (K(1/2)), A249283 (K(3/4)).

Sequence in context: A350860 A010501 A296426 * A289090 A260691 A296845

Adjacent sequences: A249279 A249280 A249281 * A249283 A249284 A249285

Keyword

nonn,cons,easy

Author

Jean-François Alcover, Oct 24 2014

Status

approved