Dec 5, 2014 · An easy way to compute the coefficients of the Taylor series of $\tanh$ is to consider that: $$\cosh(z)=\prod_{n=0}^{+\infty}\left(1+\frac{4z^2}{(2n+1)^2 \pi^2}\right ...

float fast_tanh(float x){ float x2 = x * x; float a = x * (135135.0f + x2 * (17325.0f + x2 * (378.0f + x2))); float b = 135135.0f + x2 * (62370.0f + x2 * (3150.0f + x2 * 28.0f)); return a / b; } I should add that if x might be large (not relevant for the OP), you would want to clamp the output to +/-1 for x beyond about +/-4.97.

Jun 3, 2015 · $\begingroup$ Neither is a Maclaurin series, which has to look like $\sum a_n x^n$. You can do a formal division, and obtain after some pain a few terms.

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I am a high school student and am trying to find the taylor expansion of $\tanh(x)$ in terms of a summation form. I have gotten this far, and am aware it might get complicated very quickly. If someone could aid in finishing it for me (or show a source (note I am still only a senior student so if you could not skip any steps).

Nov 15, 2015 · With l'Hôpital, compute the limit of the logarithm, that is, $$ \lim_{x\to\infty}x\log\tanh x= \lim_{x\to\infty}\frac{\log\tanh x}{1/x} $$ This is of the form $0/0 ...

Also $0\leq f(x)$, and if $0<x$: $$ (x\tanh x)' = \tanh x + x \operatorname{sech}^2x >0 . $$ It's not hard ...

Why is $\sin(\tanh x) + \sinh(\tanh x)$ almost exactly $2\tanh x$? Hot Network Questions Is it possible to combine two USB flash drives into one single partition to store a very large file, and if so, how can this be achieved?

The question: If $\sinh x-\cosh x=-5$, find $\tanh x$. Note that using the identity $$\cosh^2x -\sinh^2x=1 ,$$ we have that $(\cosh x-\sinh x )(\cosh x+\sinh x)=1 ...

Write $$\tanh(x) = \frac{1-e^{-2x}}{1+e^{-2x}}$$ Then you get an asymptotic expansion with powers of $e^{-2x}$ (which goes to $0$ as $x$ goes to infinity).