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Excerpt from On Integral Relations Involving Products of Spheroidal Functions
Meixner and Scharke[n] fbr'mathieu functions. The different integral rela tions are obtained by choosing different kernels and taking various solu tions of the spheroidal equations. Among the relations thus obtained some yield just the coefficients of the 'recurrence relations' for spheroidal functions. As in the case of Mathieu functions, these coefficients cannot be reduced to expressions which do not involve products of the functions themselves. Marx[8] obtained some of the integral relations derived here. However, our procedure enables us to avoid the use of expansion theorems for spheroidal functions, and our results are more general.
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