8.7–8.8 Associated Legendre Functions

8.70 Introduction

8.700 An associated Legendre function is a solution of the differential equation




in which ν and μ are arbitrary complex constants.

This equation is a special case of (Riemann's) hypergeometric equation (see 9.151). The points



are, in general, its singular points, specifically, its ordinary branch points.

We are interested, on the one hand, in solutions of the equation that correspond to real values of the independent variable ...

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