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1: 1.10 Functions of a Complex Variable
§1.10(vi) Multivalued Functions
Functions which have more than one value at a given point z are called multivalued (or many-valued) functions. … The function F ( z ) = ( 1 - z ) α ( 1 + z ) β is many-valued with branch points at ± 1 . …
2: 31.9 Orthogonality
The branches of the many-valued functions are continuous on the path, and assume their principal values at the beginning. …
3: 16.5 Integral Representations and Integrals
In (16.5.2)–(16.5.4) all many-valued functions in the integrands assume their principal values, and all integration paths are straight lines. …
4: 10.20 Uniform Asymptotic Expansions for Large Order
In this way there is less usage of many-valued functions. …
5: 12.10 Uniform Asymptotic Expansions for Large Parameter
In this section we give asymptotic expansions of PCFs for large values of the parameter a that are uniform with respect to the variable z , when both a and z ( = x ) are real. …
§12.10(vi) Modifications of Expansions in Elementary Functions
The following expansions hold for large positive real values of μ , uniformly for t [ - 1 + δ , ) . (For complex values of μ and t see Olver (1959).) …
6: 13.14 Definitions and Basic Properties
In general M κ , μ ( z ) and W κ , μ ( z ) are many-valued functions of z with branch points at z = 0 and z = . …