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In mathematics, '''Sonine's formula''' is any of several formulas involving [[Bessel function]]s found by [[Nikolay Yakovlevich Sonin]].
 
One such formula is the following integral formula involving a product of three Bessel functions:
 
:<math>\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}</math>
 
where Δ is the area of a triangle with given sides.
 
==References==
 
*{{Citation | last1=Stempak | first1=Krzysztof | title=A new proof of Sonine's formula | url=http://dx.doi.org/10.2307/2046994 | doi=10.2307/2046994 | id={{MR|962812}} | year=1988 | journal=[[Proceedings of the American Mathematical Society]] | issn=0002-9939 | volume=104 | issue=2 | pages=453–457}}
 
[[Category:Special hypergeometric functions]]

Revision as of 01:09, 8 March 2013

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:

0Jz(at)Jz(bt)Jz(ct)t1zdt=2z1Δ(a,b,c)2z1π1/2Γ(z+12)(abc)z

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

References

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