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* <math>\operatorname{Sinhc}(z)=\frac {{\rm KummerM}(1,\,2,\,2\,z)}{{\rm e}^z}</math>
*<math>\operatorname{Sinhc}(z)=\frac {\operatorname{HeunB} \left( 2,0,0,0,\sqrt {2}\sqrt {z} \right) }{{\rm e}^z} </math>
* <math>\operatorname{Sinhc}(z)=1/2\,\frac {{{\rm WhittakerM}(0,\,1/2,\,2\,z)}}{z} </math>
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: <math>\operatorname{Sinhc} z \approx \left(1+\frac {1}{3} z^2+\frac{2}{15}z^4+\frac {17}{315}z^6 + \frac{62}{2835} z^8 +\frac{1382}{155925} z^{10}+ \frac{21844}{6081075} z^{12} +\frac {929569}{638512875} z^{14}+O (z^{16}) \right)</math>
==Pade approximation==
<math> {\it Sinhc} \left( z \right) = \left( 1+{\frac {53272705}{360869676}}
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