of multivalued function
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1: 4.2 Definitions
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►The general logarithm function
is defined by
…This is a multivalued function of with branch point at .
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►Most texts extend the definition of the principal value to include the branch cut
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4.2.26
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►In all other cases, is a multivalued function with branch point at .
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2: 1.10 Functions of a Complex Variable
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§1.10(vi) Multivalued Functions
… ►Let be a multivalued function and be a domain. … ►Branches can be constructed in two ways: … ► ►Example
…3: 14.25 Integral Representations
4: 4.37 Inverse Hyperbolic Functions
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4.37.4
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4.37.5
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4.37.6
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►Each of the six functions is a multivalued function of .
and have branch points at ; the other four functions have branch points at .
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5: 4.23 Inverse Trigonometric Functions
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4.23.4
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4.23.5
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4.23.6
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►Each of the six functions is a multivalued function of .
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4.23.31
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6: 14.1 Special Notation
7: 14.21 Definitions and Basic Properties
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►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).
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8: 4.8 Identities
9: 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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complex plane (excluding infinity). | |
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multivalued functions. More generally, . See §1.10(vi). | |
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