Sinhc Function
Sinhc
SinhcReIm
SinhcContours
By analogy with the sinc function, define the sinhc function by
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
| [画像: intsinhc(z)dz=Shi(z)+C, ] |
(3)
|
where Shi(z) is the Shi function.
SinhcFunctionFixedPoints
The function has real fixed points at 1.31328371835... (OEIS A133916) and 2.63924951389... (OEIS A133917).
See also
Shi, Sinc Function, Tanc FunctionExplore with Wolfram|Alpha
WolframAlpha
References
Holin, H. "C++ Boost Special Functions Library." https://www.boost.org/doc/libs/1_46_1/boost/math/special_functions/sinhc.hpp.Sloane, N. J. A. Sequences A133916 and A133917 in "The On-Line Encyclopedia of Integer Sequences."Referenced on Wolfram|Alpha
Sinhc FunctionCite this as:
Weisstein, Eric W. "Sinhc Function." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/SinhcFunction.html