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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 ln z = 1 z d t t ,
Most texts extend the definition of the principal value to include the branch cutWith 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 F ( a , b ; c ; z ) 15.2(i)) in place of the more conventional F 1 2 ( 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. …