# branch conventions

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## 5 matching pages

##### 1: 10.2 Definitions

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###### Branch Conventions

…##### 2: 10.25 Definitions

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###### Branch Conventions

…##### 3: 4.12 Generalized Logarithms and Exponentials

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4.12.9
$$\psi (x)=\mathrm{\ell}+\underset{\mathrm{\ell}\text{times}}{\underset{\u23df}{\mathrm{ln}\mathrm{\cdots}\mathrm{ln}}}x,$$
$x>1$,

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4.12.10
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##### 4: 4.2 Definitions

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►This is a multivalued function of $z$ with branch point at $z=0$.
►The

*principal value*, or*principal branch*, is defined by … ►Most texts extend the definition of the principal value to include the*branch cut*… ►In all other cases, ${z}^{a}$ is a multivalued function with branch point at $z=0$. … ►With this convention, …##### 5: Mathematical Introduction

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►These include, for example, multivalued functions of complex variables, for which new definitions of branch points and principal values are supplied (§§1.10(vi), 4.2(i)); the Dirac delta (or delta function), which is introduced in a more readily comprehensible way for mathematicians (§1.17); numerically satisfactory solutions of differential and difference equations (§§2.7(iv), 2.9(i)); and numerical analysis for complex variables (Chapter 3).
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►For example, for the hypergeometric function we often use the notation $\mathbf{F}(a,b;c;z)$ (§15.2(i)) in place of the more conventional
${}_{2}{}^{}F_{1}^{}(a,b;c;z)$ or $F(a,b;c;z)$.
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►Special functions with one real variable are depicted graphically with conventional two-dimensional (2D) line graphs.
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►Another numerical convention is that decimals followed by dots are unrounded; without the dots they are rounded.
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