(35) |
These two separate ways to write the Heine identity may each be useful in numerical applications. The same thing should be possible in any of the rotational Laplace systems. For instance, in cylindrical coordinates, the infinite integrals over products of Bessel functions given by eqs. (14) and (15) can be expressed in terms of the associated toroidal functions of the first kind as well. New addition theorems and definite integrals arise as we demonstrate in the next section.