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1: 15.11 Riemann’s Differential Equation
A conformal mapping of the extended complex plane onto itself has the form …
2: 14.26 Uniform Asymptotic Expansions
The uniform asymptotic approximations given in §14.15 for P ν μ ( x ) and 𝑸 ν μ ( x ) for 1 < x < are extended to domains in the complex plane in the following references: §§14.15(i) and 14.15(ii), Dunster (2003b); §14.15(iii), Olver (1997b, Chapter 12); §14.15(iv), Boyd and Dunster (1986). …
3: 1.9 Calculus of a Complex Variable
§1.9(iv) Conformal Mapping
The extended complex plane, { } , consists of the points of the complex plane together with an ideal point called the point at infinity. …
4: 31.2 Differential Equations
All other homogeneous linear differential equations of the second order having four regular singularities in the extended complex plane, { } , can be transformed into (31.2.1). …
5: 1.12 Continued Fractions
A sequence { C n } in the extended complex plane, { } , can be a sequence of convergents of the continued fraction (1.12.3) iff …
6: 1.13 Differential Equations
A domain in the complex plane is simply-connected if it has no “holes”; more precisely, if its complement in the extended plane { } is connected. …
7: 4.40 Integrals
The results in §§4.40(ii) and 4.40(iv) can be extended to the complex plane by using continuous branches and avoiding singularities. …
8: 4.26 Integrals
The results in §§4.26(ii) and 4.26(iv) can be extended to the complex plane by using continuous branches and avoiding singularities. …
9: 3.4 Differentiation
If f can be extended analytically into the complex plane, then from Cauchy’s integral formula (§1.9(iii)) …
10: 14.21 Definitions and Basic Properties
Many of the properties stated in preceding sections extend immediately from the x -interval ( 1 , ) to the cut z -plane \ ( , 1 ] . …