By analogy with the sinc function, define the sinhc function by
(1)
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Since is not a cardinal function, the "analogy" with the sinc function is one of functional structure, not mathematical properties. It is quite possible that a better term than could be coined, although there appears to be no other name previously assigned to this function.
The function has derivative
(2)
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(3)
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where is the Shi function.
The function has real fixed points at 1.31328371835... (OEIS A133916) and 2.63924951389... (OEIS A133917).