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[[File:The cardinal hyperbolic cosine function coshc(z) plotted in the complex plane from -2-2i to 2+2i.svg|alt=The cardinal hyperbolic cosine function coshc(z) plotted in the complex plane from -2-2i to 2+2i|thumb|The cardinal hyperbolic cosine function coshc(z) plotted in the complex plane from -2-2i to 2+2i]]
In mathematics, the '''coshc function''' appears frequently in papers about [[optical scattering]],<ref>{{Cite journal |last1=den Outer |first1=P. N. |last2=Lagendijk |first2=Ad |last3=Nieuwenhuizen |first3=Th. M. |date=1993-06-01 |title=Location of objects in multiple-scattering media |url=https://opg.optica.org/abstract.cfm?URI=josaa-10-6-1209 |journal=Journal of the Optical Society of America A |language=en |volume=10 |issue=6 |pages=1209 |doi=10.1364/JOSAA.10.001209 |bibcode=1993JOSAA..10.1209D |issn=1084-7529}}</ref> Heisenberg spacetime<ref>{{Cite journal |last=Körpinar |first=Talat |date=2014 |title=New Characterizations for Minimizing Energy of Biharmonic Particles in Heisenberg Spacetime |url=http://link.springer.com/10.1007/s10773-014-2118-5 |journal=International Journal of Theoretical Physics |language=en |volume=53 |issue=9 |pages=3208–3218 |doi=10.1007/s10773-014-2118-5 |bibcode=2014IJTP...53.3208K |s2cid=121715858 |issn=0020-7748}}</ref> and [[hyperbolic geometry]].<ref>Nilgün Sönmez, [http://www.m-hikari.com/imf-password2009/37-40-2009/sonmezIMF37-40-2009.pdf A Trigonometric Proof of the Euler Theorem in Hyperbolic Geometry], International Mathematical Forum, 4, 2009, no. 38, 1877–1881</ref>{{Better source needed|reason=Predatory open-access journal|date=November 2022}} For <math>z \neq 0</math>, it is defined as<ref>{{Cite journal |last1=ten Thije Boonkkamp |first1=J. H. M. |last2=van Dijk |first2=J. |last3=Liu |first3=L. |last4=Peerenboom |first4=K. S. C. |date=2012 |title=Extension of the Complete Flux Scheme to Systems of Conservation Laws |url=http://link.springer.com/10.1007/s10915-012-9588-5 |journal=Journal of Scientific Computing |language=en |volume=53 |issue=3 |pages=552–568 |doi=10.1007/s10915-012-9588-5 |s2cid=8455136 |issn=0885-7474|doi-access=free }}</ref>
<math display="block">\operatorname{coshc}(z)=\frac {\cosh(z) }{z}</math>
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