many-valued
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6 matching pages
1: 1.10 Functions of a Complex Variable
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§1.10(vi) Multivalued Functions
►Functions which have more than one value at a given point are called multivalued (or many-valued) functions. … ►The function is many-valued with branch points at . …2: 31.9 Orthogonality
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►The branches of the many-valued functions are continuous on the path, and assume their principal values at the beginning.
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3: 16.5 Integral Representations and Integrals
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►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.
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4: 10.20 Uniform Asymptotic Expansions for Large Order
5: 12.10 Uniform Asymptotic Expansions for Large Parameter
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►In this section we give asymptotic expansions of PCFs for large values of the parameter that are uniform with respect to the variable , when both and
are real.
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►The following expansions hold for large positive real values of , uniformly for .
(For complex values of and see Olver (1959).)
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