Showing content from https://dlmf.nist.gov/4.29 below:
§4.29 Graphics ⣠Hyperbolic Functions ⣠Chapter 4 Elementary Functions
§4.29 Graphics â
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Referenced by:
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§4.37(ii)
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Permalink:
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http://dlmf.nist.gov/4.29
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See also:
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Annotations for Ch.4
Contents
- §4.29(i) Real Arguments
- §4.29(ii) Complex Arguments
§4.29(i) Real Arguments â
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Keywords:
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graphics, hyperbolic functions, inverse hyperbolic functions, real argument
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Notes:
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These graphs were produced at NIST.
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http://dlmf.nist.gov/4.29.i
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Annotations for §4.29 and Ch.4
Figure 4.29.1: sinh â¡ x and cosh â¡ x . Magnify â
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Symbols:
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cosh â¡ z : hyperbolic cosine function, sinh â¡ z : hyperbolic sine function and x : real variable
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A&S Ref:
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AMS55 (Figure 4.6)
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http://dlmf.nist.gov/4.29.F1
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pdf, png
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Annotations for §4.29(i), §4.29 and Ch.4
Figure 4.29.2: Principal values of arcsinh â¡ x and arccosh â¡ x . ( arccosh â¡ x is complex when x < 1 .) Magnify â
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Symbols:
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arccosh â¡ z : inverse hyperbolic cosine function, arcsinh â¡ z : inverse hyperbolic sine function and x : real variable
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A&S Ref:
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AMS55 (Figure 4.8)
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http://dlmf.nist.gov/4.29.F2
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Encodings:
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pdf, png
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See also:
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Annotations for §4.29(i), §4.29 and Ch.4
Figure 4.29.3: tanh â¡ x and coth â¡ x . Magnify â
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Symbols:
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coth â¡ z : hyperbolic cotangent function, tanh â¡ z : hyperbolic tangent function and x : real variable
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A&S Ref:
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AMS55 (Figure 4.6)
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Permalink:
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http://dlmf.nist.gov/4.29.F3
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Encodings:
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pdf, png
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See also:
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Annotations for §4.29(i), §4.29 and Ch.4
Figure 4.29.4: Principal values of arctanh â¡ x and arccoth â¡ x . ( arctanh â¡ x is complex when x < â 1 or x > 1 , and arccoth â¡ x is complex when â 1 < x < 1 .) Magnify â
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Symbols:
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arccoth â¡ z : inverse hyperbolic cotangent function, arctanh â¡ z : inverse hyperbolic tangent function and x : real variable
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A&S Ref:
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AMS55 (Figure 4.8)
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Permalink:
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http://dlmf.nist.gov/4.29.F4
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Encodings:
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pdf, png
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See also:
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Annotations for §4.29(i), §4.29 and Ch.4
Figure 4.29.5: csch â¡ x and sech â¡ x . Magnify â
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Symbols:
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csch â¡ z : hyperbolic cosecant function, sech â¡ z : hyperbolic secant function and x : real variable
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A&S Ref:
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AMS55 (Figure 4.6)
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Permalink:
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http://dlmf.nist.gov/4.29.F5
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Encodings:
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pdf, png
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See also:
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Annotations for §4.29(i), §4.29 and Ch.4
Figure 4.29.6: Principal values of arccsch â¡ x and arcsech â¡ x . ( arcsech â¡ x is complex when x < 0 and x > 1 .) Magnify â
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Symbols:
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arccsch â¡ z : inverse hyperbolic cosecant function, arcsech â¡ z : inverse hyperbolic secant function and x : real variable
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A&S Ref:
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AMS55 (Figure 4.8)
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Permalink:
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http://dlmf.nist.gov/4.29.F6
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Encodings:
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pdf, png
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See also:
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Annotations for §4.29(i), §4.29 and Ch.4
§4.29(ii) Complex Arguments â
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Keywords:
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complex argument, conformal maps, graphics, hyperbolic functions, inverse hyperbolic functions
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Permalink:
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http://dlmf.nist.gov/4.29.ii
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See also:
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Annotations for §4.29 and Ch.4
The conformal mapping w = sinh â¡ z is obtainable from Figure 4.15.7 by rotating both the w -plane and the z -plane through an angle 1 2 â¢ Ï , 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)â(4.28.13).
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