Dual Trigonometrical Series

In a recent joint paper with J. C. Cooke [1], we have given a method of determining the coefficients a n in the “dual” Fourier-Bessel series where −1 ≤ p ≤, F ( r ) is specified and α n is a positive root of J v (α n α) = 0. This method reduced the problem to the solution of an infinite set of algebraical equations and it was shown that, under certain circumstances, numerical values for the coefficients could be obtained fairly readily.