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30 Spheroidal Wave FunctionsProperties

§30.6 Functions of Complex Argument

The solutions

30.6.1 Psnm(z,γ2),

of (30.2.1) with μ=m and λ=λnm(γ2) are real when z(1,), and their principal values (§4.2(i)) are obtained by analytic continuation to \(-,1].

Relations to Associated Legendre Functions


Values on (-1,1)

For further properties see Arscott (1964b).

For results for Equation (30.2.1) with complex parameters see Meixner and Schäfke (1954).