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== Properties ==
The first-order derivative is given by
:<math> \operatorname{sinhc}^\prime(z)=\frac {\cosh(z)}{z} - \frac {\sinh(z)}{z^2} </math>
The [[Taylor series]] expansion is<math display="block">\sum_{i=0}^\infty \frac{z^{2i}}{(2i+1)!}.</math>The [[Padé approximant]] is<math display="block"> \operatorname{sinhc} \left( z \right) = \left( 1+{\frac {53272705}{360869676}}
\,{z}^{2}+{\frac {38518909}{7217393520}}\,{z}^{4}+{\frac {269197963}{
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