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1: 22.22 Software
§22.22(iii) Complex Argument
2: 20.16 Software
§20.16(iii) Complex Argument and/or Parameter
3: 30.6 Functions of Complex Argument
§30.6 Functions of Complex Argument
The solutions …
30.6.3 𝒲 { Ps n m ( z , γ 2 ) , Qs n m ( z , γ 2 ) } = ( - 1 ) m ( n + m ) ! ( 1 - z 2 ) ( n - m ) ! A n m ( γ 2 ) A n - m ( γ 2 ) ,
4: 23.24 Software
§23.24(iii) Complex Argument
5: 16.27 Software
§16.27(iii) Complex Argument and/or Parameters
6: 4.3 Graphics
§4.3(ii) Complex Arguments: Conformal Maps
§4.3(iii) Complex Arguments: Surfaces
See accompanying text
Figure 4.3.3: ln ( x + i y ) (principal value). … Magnify 3D Help
See accompanying text
Figure 4.3.4: e x + i y . Magnify 3D Help
7: 4.29 Graphics
§4.29(ii) Complex Arguments
8: 4.15 Graphics
§4.15(ii) Complex Arguments: Conformal Maps
§4.15(iii) Complex Arguments: Surfaces
The corresponding surfaces for arccos ( x + i y ) , arccot ( x + i y ) , arcsec ( x + i y ) 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).
9: 10.77 Software
§10.77(iv) Bessel Functions–Integer or Half-Integer Order and Complex Arguments, including Kelvin Functions
§10.77(v) Bessel Functions–Real Order and Complex Argument (including Hankel Functions)
§10.77(vii) Bessel Functions–Complex Order and Real Argument
§10.77(viii) Bessel Functions–Complex Order and Argument
10: 14.26 Uniform Asymptotic Expansions
For an extension of §14.15(iv) to complex argument and imaginary parameters, see Dunster (1990b). …