2014年12月5日 · 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 …

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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 ...

2015年6月3日 · $\begingroup$ 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.

First of all notice that to keep consistency $$\tanh\theta = \dfrac{e^x-e^{-x}}{e^x+e^{-x}}$$ Should have been $$\tanh(x) = \dfrac{e^x-e^{-x}}{e^x+e^{-x}}$$ Same with your other two functions. …

My maths professor Siegfried Goeldner who got his PhD in mathematics at the Courant Institute at New York University under one of the German refugees from Goetingen, in 1960, …

2017年6月14日 · Stack Exchange Network. Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for …

2015年11月15日 · 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 ...