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21—30 of 242 matching pages
21: 2.2 Transcendental Equations
22: 4.29 Graphics
23: 4.12 Generalized Logarithms and Exponentials
24: 22.1 Special Notation
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►The functions treated in this chapter are the three principal Jacobian elliptic functions , , ; the nine subsidiary Jacobian elliptic functions , , , , , , , , ; the amplitude function ; Jacobi’s epsilon and zeta functions and .
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25: 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).
The principal branches of and are real when , and .
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26: 27.11 Asymptotic Formulas: Partial Sums
27: 4.15 Graphics
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►Figure 4.15.7 illustrates the conformal mapping of the strip onto the whole -plane cut along the real axis from to and to , where and (principal value).
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28: 4.23 Inverse Trigonometric Functions
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§4.23(ii) Principal Values
… ►Compare the principal value of the logarithm (§4.2(i)). … ►The principal values of the inverse cosecant, secant, and cotangent are given by … ►Graphs of the principal values for real arguments are given in §4.15. … ►Throughout this subsection all quantities assume their principal values. …29: 10.25 Definitions
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