Tanhc Function
المؤلف:
Sloane, N. J. A
المصدر:
Sequences A133918 and A133919 in "The On-Line Encyclopedia of Integer Sequences."
الجزء والصفحة:
...
3-6-2019
2140
Tanhc Function
By analogy with the tanc function, define the tanhc function by
![tanhc(z)=<span style=]() {(tanhz)/z for z!=0; 1 for z=0. " src="http://mathworld.wolfram.com/images/equations/TanhcFunction/NumberedEquation1.gif" style="height:60px; width:181px" /> |
(1)
|
It has derivative
 |
(2)
|
The indefinite integral can apparently not be done in closed form in terms of conventionally defined functions.
It has maximum at 
, and positive inflection point at the solution to
 |
(3)
|
which is 0.919937667... (OEIS A133919).
It has a unique real fixed point at 0.82242927726... (OEIS A133918).
REFERENCES:
Sloane, N. J. A. Sequences A133918 and A133919 in "The On-Line Encyclopedia of Integer Sequences."
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