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Table of Integrals, Series, and Products, 8th Edition by Daniel Zwillinger

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8.84 Conical functions

8.840 Let us set

ν=12+iλ,

si1510_e

where λ is a real parameter, in the defining differential equation 8.700 1 for associated Legendre functions. We then obtain the differential equation of the so-called conical functions. A conical function is a special case of the associated Legendre function. However, the Legendre functions

P12+iλ(x), Q12+iλ(x)

si1511_e

have certain peculiarities that make us distinguish them as a special class—the class of conical functions. The most important of these peculiarities is the following

8.841 The functions ...

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