In mathematics, the coshc function appears frequently in papers about
optical scattering
Scattering is a term used in physics to describe a wide range of physical processes where moving particles or radiation of some form, such as light or sound, are forced to deviate from a straight trajectory by localized non-uniformities (including ...
, Heisenberg spacetime and
hyperbolic geometry. For
, it is defined as
It is a solution of the following differential equation:
Properties
The first-order derivative is given by
:
The
Taylor series
In mathematics, the Taylor series or Taylor expansion of a function is an infinite sum of terms that are expressed in terms of the function's derivatives at a single point. For most common functions, the function and the sum of its Taylor serie ...
expansion is
The
Padé approximant is
In terms of other special functions
*
, where
is Kummer's
confluent hypergeometric function
In mathematics, a confluent hypergeometric function is a solution of a confluent hypergeometric equation, which is a degenerate form of a hypergeometric differential equation where two of the three regular singularities merge into an irregular ...
.
*
, where
is the biconfluent
Heun function.
*
, where
is a
Whittaker function.
Gallery
{,
,
,
,
See also
*
Tanc function
*
Tanhc function
*
Sinhc function In mathematics, the sinhc function appears frequently in papers about optical scattering, Heisenberg spacetime and hyperbolic geometry. For z \neq 0, it is defined as
\operatorname(z)=\frac
The sinhc function is the hyperbolic analogue of the sinc ...
References
Special functions