A249282 - OEIS

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

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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