# Connect the curve 4

Calculus Level 5

The figure shows the curves of $$y=\cos { \left( \cos { \left( x \right) } \right) }$$ in blue and $$y=\sin { \left( \sin { \left( x \right) } \right) }$$ in red.

It also shows a green region enclosed between these graphs in domain $$\left[ 0,2\pi \right]$$.

If the area of the green region is $A{ \pi }^{ B }{ J }_{ \alpha }\left( n \right)$

Find $$A+B+\alpha+n$$

Details and Assumptions

1. $${ J }_{ \alpha }\left( n \right)$$ is a Bessel function of the first kind.

Or $J_{ \alpha }(n)=\sum _{ m=0 }^{ \infty } \frac { (-1)^{ m } }{ m!\, \Gamma (m+\alpha +1) } { \left( \frac { n}{ 2 } \right) }^{ 2m+\alpha }$

1. $$A$$, $$B$$, $$\alpha$$ and $$n$$ are integers.

2. $$\alpha<n$$

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