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 | ||
$$\mathrm{tanhc}(z) = \dfrac{\mathrm{tanh}(z)}{z}.$$ | $$\mathrm{tanhc}(z) = \dfrac{\mathrm{tanh}(z)}{z}.$$ | ||
| + | |||
| + | =Properties= | ||
| + | <div class="toccolours mw-collapsible mw-collapsed"> | ||
| + | <strong>Theorem:</strong> The following formula holds: | ||
| + | $$\dfrac{d}{dz} \mathrm{tanhc}(z) = \dfrac{\mathrm{sech}^2(z)}{z}-\dfrac{\mathrm{tanh(z)}}{z^2}.$$ | ||
| + | <div class="mw-collapsible-content"> | ||
| + | <strong>Proof:</strong> █ | ||
| + | </div> | ||
| + | </div> | ||
<center>{{:*-c functions footer}}</center> | <center>{{:*-c functions footer}}</center> | ||
Revision as of 23:14, 19 May 2015
The $\mathrm{tanhc}$ function is defined by $$\mathrm{tanhc}(z) = \dfrac{\mathrm{tanh}(z)}{z}.$$
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: █
