# many-valued function

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6 matching pages ♦

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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 $z$ are called*multivalued*(or*many-valued*) functions. … ►The function $F(z)={(1-z)}^{\alpha}{(1+z)}^{\beta}$ is many-valued with branch points at $\pm 1$. …##### 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 $a$ that are uniform with respect to the variable $z$, when both $a$ and $z$
$(=x)$ are real.
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###### §12.10(vi) Modifications of Expansions in Elementary Functions

… ►The following expansions hold for large positive real values of $\mu $, uniformly for $t\in [-1+\delta ,\mathrm{\infty})$. (For complex values of $\mu $ and $t$ see Olver (1959).) … ►##### 6: 13.14 Definitions and Basic Properties

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►In general ${M}_{\kappa ,\mu}\left(z\right)$ and ${W}_{\kappa ,\mu}\left(z\right)$ are many-valued functions of $z$ with branch points at $z=0$ and $z=\mathrm{\infty}$.
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