Special cases of general formulas due to Bessel.
 |
where 
is a Bessel function of the first kind.
Now, let 
and 
.
Then
![J_0(2isqrt(z))=1/piint_0^pie^((1+z)costheta)cos[(1-z)sintheta]dtheta.](/images/equations/CatalanIntegrals/NumberedEquation2.svg) |
Catalan Integrals
See also
Bessel Function of the First KindExplore with Wolfram|Alpha
Cite this as:
Weisstein, Eric W. "Catalan Integrals." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/CatalanIntegrals.html