principal branch
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31—40 of 178 matching pages
31: 5.17 Barnes’ -Function (Double Gamma Function)
32: 4.7 Derivatives and Differential Equations
33: 4.19 Maclaurin Series and Laurent Series
34: 10.25 Definitions
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βΊ
§10.25(ii) Standard Solutions
… βΊIn particular, the principal branch of is defined in a similar way: it corresponds to the principal value of , is analytic in , and two-valued and discontinuous on the cut . … βΊThe principal branch corresponds to the principal value of the square root in (10.25.3), is analytic in , and two-valued and discontinuous on the cut . …35: 7.17 Inverse Error Functions
36: 4.9 Continued Fractions
37: 10.8 Power Series
38: 4.23 Inverse Trigonometric Functions
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βΊThe principal values (or principal branches) of the inverse sine, cosine, and tangent are obtained by introducing cuts in the -plane as indicated in Figures 4.23.1(i) and 4.23.1(ii), and requiring the integration paths in (4.23.1)–(4.23.3) not to cross these cuts.
…The principal branches are denoted by , , , respectively.
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βΊ
4.23.24
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βΊ
4.23.25
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βΊ
4.23.36
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39: 5.9 Integral Representations
40: 15.2 Definitions and Analytical Properties
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βΊ
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βΊagain with analytic continuation for other values of , and with the principal branch defined in a similar way.
βΊExcept where indicated otherwise principal branches of and are assumed throughout the DLMF.
βΊThe difference between the principal branches on the two sides of the branch cut (§4.2(i)) is given by
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βΊThe principal branch of is an entire function of , , and .
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