branch conventions

(0.001 seconds)

5 matching pages

3: 4.12 Generalized Logarithms and Exponentials
4.12.9 $\psi(x)=\ell+\underbrace{\ln\cdots\ln}_{\ell\text{ times}}x,$ $x>1$,
4.12.10 $0\leq\underbrace{\ln\cdots\ln}_{\ell\text{times}}x<1.$
4: 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 … Most texts extend the definition of the principal value to include the branch cutIn all other cases, $z^{a}$ is a multivalued function with branch point at $z=0$. … With this convention, …
5: 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}\left(a,b;c;z\right)$15.2(i)) in place of the more conventional ${{}_{2}F_{1}}\left(a,b;c;z\right)$ or $F\left(a,b;c;z\right)$. … 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. …