Sonine formula

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In mathematics, Sonine's formula is any of several formulas involving Bessel functions found by Nikolay Yakovlevich Sonin.

One such formula is the following integral formula involving a product of three Bessel functions:

\int_0^\infty J_z(at) J_z(bt)J_z(ct) t^{1-z}\,dt = \frac{2^{z-1}\Delta(a,b,c)^{2z-1}}{\pi^{1/2}\Gamma(z+\tfrac 12)(abc)^z}

where Δ is the area of a triangle with given sides.