# branch conventions

♦
4 matching pages ♦

(0.001 seconds)

## 4 matching pages

##### 1: 10.2 Definitions

…
►

###### Branch Conventions

…##### 2: 10.25 Definitions

…
►

###### Branch Conventions

…##### 3: 4.2 Definitions

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

*principal value*, or*principal branch*, is defined by ►
4.2.2
$$\mathrm{ln}z={\int}_{1}^{z}\frac{dt}{t},$$

…
►Most texts extend the definition of the principal value to include the *branch cut*… ►With this convention, …##### 4: Mathematical Introduction

…
►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).
…
►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 $F(a,b;c;z)$.
…
►Special functions with one real variable are depicted graphically with conventional two-dimensional (2D) line graphs.
…
►Another numerical convention is that decimals followed by dots are unrounded; without the dots they are rounded.
…