The sinhc function is defined by analogy with the sinc
function as
 |
(1)
|
The identity 
shows that both are even
functions and entire functions. Unlike the
sinc function, 
for every real number 
.
The function has derivative
 |
(2)
|
for 
,
with 
,
and indefinite integral
 |
(3)
|
where 
is the Shi function.
The function has exactly two real fixed points at 1.31328371835... (OEIS A133916)
and 2.63924951389... (OEIS A133917).
See also
Shi,
Sinc Function,
Tanc Function
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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 Function
Cite this as:
Weisstein, Eric W. "Sinhc Function." From
MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/SinhcFunction.html
Subject classifications
