of complex argument

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3: 30.6 Functions of Complex Argument
§30.6 Functions of ComplexArgument
The solutions …
30.6.3 $\mathscr{W}\left\{\mathit{Ps}^{m}_{n}\left(z,\gamma^{2}\right),\mathit{Qs}^{m}% _{n}\left(z,\gamma^{2}\right)\right\}=\frac{(-1)^{m}(n+m)!}{(1-z^{2})(n-m)!}A_% {n}^{m}(\gamma^{2})A_{n}^{-m}(\gamma^{2}),$
30.6.4 $\mathit{Ps}^{m}_{n}\left(x\pm\mathrm{i}0,\gamma^{2}\right)=(\mp\mathrm{i})^{m}% \mathsf{Ps}^{m}_{n}\left(x,\gamma^{2}\right),$
30.6.5 $\mathit{Qs}^{m}_{n}\left(x\pm\mathrm{i}0,\gamma^{2}\right)={(\mp\mathrm{i})^{m% }\left(\mathsf{Qs}^{m}_{n}\left(x,\gamma^{2}\right)\mp\tfrac{1}{2}\mathrm{i}% \pi\mathsf{Ps}^{m}_{n}\left(x,\gamma^{2}\right)\right)}.$
8: 4.15 Graphics
§4.15(iii) ComplexArguments: Surfaces
The corresponding surfaces for $\operatorname{arccos}\left(x+iy\right)$, $\operatorname{arccot}\left(x+iy\right)$, $\operatorname{arcsec}\left(x+iy\right)$ can be visualized from Figures 4.15.9, 4.15.11, 4.15.13 with the aid of equations (4.23.16)–(4.23.18).
10: 14.26 Uniform Asymptotic Expansions
For an extension of §14.15(iv) to complex argument and imaginary parameters, see Dunster (1990b). …