4 Elementary FunctionsHyperbolic Functions

§4.29 Graphics

Contents
  1. §4.29(i) Real Arguments
  2. §4.29(ii) Complex Arguments

§4.29(i) Real Arguments

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Figure 4.29.1: sinh⁡x and cosh⁡x. Magnify
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Figure 4.29.2: Principal values of arcsinh⁡x and arccosh⁡x. (arccosh⁡x is complex when x<1.) Magnify
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Figure 4.29.3: tanh⁡x and coth⁡x. Magnify
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Figure 4.29.4: Principal values of arctanh⁡x and arccoth⁡x. (arctanh⁡x is complex when x<−1 or x>1, and arccoth⁡x is complex when −1<x<1.) Magnify
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Figure 4.29.5: csch⁡x and sech⁡x. Magnify
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Figure 4.29.6: Principal values of arccsch⁡x and arcsech⁡x. (arcsech⁡x is complex when x<0 and x>1.) Magnify

§4.29(ii) Complex Arguments

The conformal mapping w=sinh⁡z is obtainable from Figure 4.15.7 by rotating both the w-plane and the z-plane through an angle 12⁢π, 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. They can be visualized with the aid of equations (4.28.8)–(4.28.13).