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:
| infty | |
| \int | |
| 0 |
Jz(at)Jz(bt)Jz(ct)t1-zdt=
| 2z-1\Delta(a,b,c)2z-1 | |
| \pi1/2\Gamma(z+\tfrac12)(abc)z |
where Δ is the area of a triangle with given sides.