# many-valued function

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## 6 matching pages

##### 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 $F(z)=(1-z)^{\alpha}(1+z)^{\beta}$ is many-valued with branch points at $\pm 1$. …
##### 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: 13.14 Definitions and Basic Properties
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 $z=\infty$. …
##### 6: 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 $\mu$, uniformly for $t\in[-1+\delta,\infty)$. (For complex values of $\mu$ and $t$ see Olver (1959).) …