Product of Bessel Functions of the First Kind

[natski]

Hi all,

I have been looking through various textbooks for a formula for combining the product of two Bessel functions of the first kind into one new Bessel function. I have:

z = J_0(x) J_0(y)

and I am looking for an equivalent expression like:

z = J_m( f(x,y) )

Does anyone know whether this is possible?

Thanks,

Natski