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In mathematics, the '''Sinhc function''' appears frequently in papers about optical scattering,<ref>PN Den Outer, TM Nieuwenhuizen, A Lagendijk, Location of objects in multiple-scattering media, JOSA A, Vol. 10, Issue 6, pp. 1209–1218 (1993)</ref> Heisenberg Spacetime<ref>T Körpinar, New characterizations for minimizing energy of biharmonic particles in Heisenberg spacetime - International Journal of Theoretical Physics, 2014 - Springer</ref> and hyperbolic geometry.<ref>Nilg¨un S¨onmez, A Trigonometric Proof of the Euler Theorem in Hyperbolic Geometry, International Mathematical Forum, 4, 2009, no. 38, 1877–1881</ref> It is defined as<ref>JHM ten Thije Boonkkamp, J van Dijk, L Liu, Extension of the complete flux scheme to systems of conservation laws, J Sci Comput (2012) 53:552–568, DOI 10.1007/s10915-012-9588-5</ref><ref>Weisstein, Eric W. "Sinhc Function." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/SinhcFunction.html</ref>
<math display="block">\operatorname{Sinhc}(z)=\frac {\sinh(z) }{z}</math>
[[File:The cardinal hyperbolic sine function sinhc(z) plotted in the complex plane from -2-2i to 2+2i.svg|alt=The cardinal hyperbolic sine function sinhc(z) plotted in the complex plane from -2-2i to 2+2i|thumb|The cardinal hyperbolic sine function sinhc(z) plotted in the complex plane from -2-2i to 2+2i]]
It is a solution of the following differential equation:
<math display="block">w(z) z-2\,\frac {d}{dz} w (z) -z \frac {d^2}{dz^2} w (z) =0</math>
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