Tanhc Function
Tanhc
TanhcReIm
TanhcContours
By analogy with the tanc function, define the tanhc function by
It has derivative
The indefinite integral can apparently not be done in closed form in terms of conventionally defined functions.
It has maximum at z=0, and positive inflection point at the solution to
| xsech^2x^2-tanhx+x^2sech^2xtanhx=0, |
(3)
|
which is 0.919937667... (OEIS A133919).
TanhcFunctionFixedPoint
It has a unique real fixed point at 0.82242927726... (OEIS A133918).
See also
Sinhc Function, Tanc FunctionExplore with Wolfram|Alpha
WolframAlpha
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References
Sloane, N. J. A. Sequences A133918 and A133919 in "The On-Line Encyclopedia of Integer Sequences."Referenced on Wolfram|Alpha
Tanhc FunctionCite this as:
Weisstein, Eric W. "Tanhc Function." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/TanhcFunction.html