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Catalan Integrals


Special cases of general formulas due to Bessel.

 J_0(sqrt(z^2-y^2))=1/piint_0^pie^(ycostheta)cos(zsintheta)dtheta,

where J_0(z) is a Bessel function of the first kind. Now, let z=1-z^' and y=1+z^'. Then

 J_0(2isqrt(z))=1/piint_0^pie^((1+z)costheta)cos[(1-z)sintheta]dtheta.

See also

Bessel Function of the First Kind

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Cite this as:

Weisstein, Eric W. "Catalan Integrals." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/CatalanIntegrals.html

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