The On-Line Encyclopedia of Integer Sequences (OEIS)

A352615 revision #17

A352615

Decimal expansion of Integral_{0<=x,y<=Pi/2}sqrt(1-cos^2(x)*cos^2(y))dxdy.

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

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OFFSET

1,1

LINKS

Table of n, a(n) for n=1..105.

FORMULA

Equals Sum _{n>=0}(Pi^2/(4*(2*n-1))(binomial(2*n,n)/4^n)^3)

Equals (E(a)-K(a))^2+E(a)^2 where a=1/sqrt(2) and E (resp. K) is the complete elliptic integral of the second (resp. first) kind.

EXAMPLE

2.0776814600281582057831205567855290128037790576247...

MAPLE

a:=1/sqrt(2):evalf((EllipticE(a)-EllipticK(a))^2+EllipticE(a)^2, 50);