inverse hyperbolic functions
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11: 4.45 Methods of Computation
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Hyperbolic and Inverse Hyperbolic Functions
… ►Similarly for the hyperbolic and inverse hyperbolic functions; compare (4.28.1)–(4.28.7), §4.37(iv), and (4.37.7)–(4.37.9). …12: 19.17 Graphics
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►Because the -function is homogeneous, there is no loss of generality in giving one variable the value or (as in Figure 19.3.2).
…The case corresponds to elementary functions.
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13: 19.2 Definitions
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19.2.17
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►In (19.2.18)–(19.2.22) the inverse trigonometric and hyperbolic functions assume their principal values (§§4.23(ii) and 4.37(ii)).
When and are positive, is an inverse circular function if and an inverse hyperbolic function (or logarithm) if :
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19.2.19
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19.2.20
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14: 19.12 Asymptotic Approximations
15: 19.26 Addition Theorems
16: 4.32 Inequalities
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4.32.4
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17: 19.11 Addition Theorems
18: 19.20 Special Cases
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19.20.5
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19.20.13
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►When the variables are real and distinct, the various cases of are called circular (hyperbolic) cases if is positive (negative), because they typically occur in conjunction with inverse circular (hyperbolic) functions.
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19.20.20
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19.20.21
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