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21: 4.46 Tables
§4.46 Tables
… ►(These roots are zeros of the Bessel function ; see §10.21.) ►For 10S values of the first five complex roots of , , and , for selected positive values of , see Fettis (1976). …22: 4.38 Inverse Hyperbolic Functions: Further Properties
§4.38 Inverse Hyperbolic Functions: Further Properties
►§4.38(i) Power Series
… ►§4.38(ii) Derivatives
… ►§4.38(iii) Addition Formulas
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4.38.16
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23: 4.29 Graphics
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§4.29(i) Real Arguments
… ► ►§4.29(ii) Complex Arguments
►The conformal mapping is obtainable from Figure 4.15.7 by rotating both the -plane and the -plane through an angle , compare (4.28.8). ►The surfaces for the complex hyperbolic and inverse hyperbolic functions are similar to the surfaces depicted in §4.15(iii) for the trigonometric and inverse trigonometric functions. …24: 4.43 Cubic Equations
§4.43 Cubic Equations
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4.43.2
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, , and , with , when .
, , and , with , when , , and .
, , and , with , when .
25: 4.28 Definitions and Periodicity
§4.28 Definitions and Periodicity
… ►Relations to Trigonometric Functions
… ►As a consequence, many properties of the hyperbolic functions follow immediately from the corresponding properties of the trigonometric functions. ►Periodicity and Zeros
►The functions and have period , and has period . …26: 7.8 Inequalities
27: 20.10 Integrals
28: 4.1 Special Notation
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►The main purpose of the present chapter is to extend these definitions and properties to complex arguments .
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►; the hyperbolic trigonometric (or just hyperbolic) functions , , , , , ; the inverse hyperbolic functions , , etc.
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integers. | |
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29: 28.26 Asymptotic Approximations for Large
30: 8 Incomplete Gamma and Related
Functions
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