Difference between revisions of "Tanhc"
From specialfunctionswiki
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The $\mathrm{tanhc}$ function is defined by | The $\mathrm{tanhc}$ function is defined by | ||
$$\mathrm{tanhc}(z) = \dfrac{\mathrm{tanh}(z)}{z}.$$ | $$\mathrm{tanhc}(z) = \dfrac{\mathrm{tanh}(z)}{z}.$$ | ||
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| + | <div align="center"> | ||
| + | <gallery> | ||
| + | File:Complex tanhc.png|[[Domain coloring]] of [[analytic continuation]] of $\mathrm{tanhc}(z)$. | ||
| + | </gallery> | ||
| + | </div> | ||
=Properties= | =Properties= | ||
Revision as of 23:16, 19 May 2015
The $\mathrm{tanhc}$ function is defined by $$\mathrm{tanhc}(z) = \dfrac{\mathrm{tanh}(z)}{z}.$$
Domain coloring of analytic continuation of $\mathrm{tanhc}(z)$.
Properties
Theorem: The following formula holds: $$\dfrac{d}{dz} \mathrm{tanhc}(z) = \dfrac{\mathrm{sech}^2(z)}{z}-\dfrac{\mathrm{tanh(z)}}{z^2}.$$
Proof: █
