Sonine formula

Template:Short description 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:

${\int }_0^{\mathrm{\infty }}{J}_z(at)J_z(bt)J_z(ct)t^{1-z}dt=\frac{2^{z-1}\mathrm{\Delta }(a,b,c{)}^{2z-1}}{{\pi }^{1/2}\mathrm{\Gamma }(z+\frac{1}{2})(abc{)}^z}$

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

References

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