of multivalued function
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… ►The general logarithm function is defined by …This is a multivalued function of with branch point at . … ►Most texts extend the definition of the principal value to include the branch cut … ►
4.2.26 .… ►In all other cases, is a multivalued function with branch point at . …
§1.10(vi) Multivalued Functions… ►Let be a multivalued function and be a domain. … ►Branches can be constructed in two ways: … ► ►
… ►where the multivalued functions have their principal values when and are continuous in . …
4.37.6… ►Each of the six functions is a multivalued function of . and have branch points at ; the other four functions have branch points at . …
4.23.6… ►Each of the six functions is a multivalued function of . … ►
… ►When is complex , , and are defined by (14.3.6)–(14.3.10) with replaced by : the principal branches are obtained by taking the principal values of all the multivalued functions appearing in these representations when , and by continuity elsewhere in the -plane with a cut along the interval ; compare §4.2(i). …
… ►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). … ►
complex plane (excluding infinity).
multivalued functions. More generally, . See §1.10(vi).