A118178 integral in closed form

[Max]

Eric,

I have not got the closed form yet but I found the following
connection to the sequence A092765. The integral in question is equal
to

2 * Pi * SUM[n=0..+oo] binomial(1/2,n) * 4^(-n) * A092765(n)

I am going to submit some clarifying comments to A092765.

btw, there is a missing integral sign in the formula (11) at
http://mathworld.wolfram.com/EightCurve.html

Max

On 4/18/06, Eric W. Weisstein <eric at weisstein.com> wrote:
> Can anyone get
>
> http://www.research.att.com/~njas/sequences/A118178
>
> 4*Integrate[Sqrt[4*Sin[t]^4-5*Sin[t]^2+2], {t, 0, Pi/2}]
>
> in closed form?
>
> Cheers,
> -Eric
>
>