General solution of the Feller equation

Using solution (1.37) in definition (1.4), one has the angular momentum correlation function 

In order to determine the actual strength of collisions, it is desirable to have a general solution of the Feller equation that holds for any y. Consider the problem of the eigenvalues of the integral operator L, which appears in the Feller equation 

In view of multiplicity of Eq. (1.13) it is expedient to seek the solution in the form 

In this case Fourier transformation (1.43) gives for the case of two dimensions (r = 2) 

After differentiating the expression with respect to y and introducing new variables U = yu and V = yv, we divide them 

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