Sinhc Function


By analogy with the sinc function, define the sinhc function by

 sinhc(z)={(sinhz)/z   for z!=0; 1   for z=0.

Since sinhx/x 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 sinhc(x) could be coined, although there appears to be no other name previously assigned to this function.

The function has derivative


and indefinite integral


where Shi(z) is the Shi function.


The function has real fixed points at 1.31328371835... (OEIS A133916) and 2.63924951389... (OEIS A133917).

See also

Shi, Sinc Function, Tanc Function

Explore with Wolfram|Alpha


Holin, H. "C++ Boost Special Functions Library.", N. J. A. Sequences A133916 and A133917 in "The On-Line Encyclopedia of Integer Sequences."

Referenced on Wolfram|Alpha

Sinhc Function

Cite this as:

Weisstein, Eric W. "Sinhc Function." From MathWorld--A Wolfram Web Resource.

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