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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

See accompanying text
Figure 4.29.1: sinhx and coshx. Magnify
See accompanying text
Figure 4.29.2: Principal values of arcsinhx and arccoshx. (arccoshx is complex when x<1.) Magnify
See accompanying text
Figure 4.29.3: tanhx and cothx. Magnify
See accompanying text
Figure 4.29.4: Principal values of arctanhx and arccothx. (arctanhx is complex when x<1 or x>1, and arccothx is complex when 1<x<1.) Magnify
See accompanying text
Figure 4.29.5: cschx and sechx. Magnify
See accompanying text
Figure 4.29.6: Principal values of arccschx and arcsechx. (arcsechx is complex when x<0 and x>1.) Magnify

§4.29(ii) Complex Arguments

The conformal mapping w=sinhz is obtainable from Figure 4.15.7 by rotating both the w-plane and the z-plane through an angle 12π, 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).