Sonine formula

{{Short description|Mathematical formula involving Bessel functions}}

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:

:$\backslash int\_0^\backslash infty\; J\_z(at)\; J\_z(bt)J\_z(ct)\; t^\{1-z\}\backslash ,dt\; =\; \backslash frac\{2^\{z-1\}\backslash Delta(a,b,c)^\{2z-1\}\}\{\backslash pi^\{1/2\}\backslash Gamma(z+\backslash tfrac\; 12)(abc)^z\}$

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