From Wikipedia, the free encyclopedia
In mathematics, the tanc function is defined for
as[1]
Tanc 2D plot
Tanc'(z) 2D plot
Tanc integral 2D plot
Tanc integral 3D plot
Properties
The first-order derivative of the tanc function is given by
![{\displaystyle {\frac {\sec ^{2}(z)}{z}}-{\frac {\tan(z)}{z^{2}}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/a9de276e977499dc57d5e7723d9be423f79e706d)
The Taylor series expansion is
which leads to the series expansion of the integral as
The Padé approximant is
In terms of other special functions
, where
is Kummer's confluent hypergeometric function.
, where
is the biconfluent Heun function.
, where
is a Whittaker function.
Gallery
Tanc abs complex 3D
|
Tanc Im complex 3D plot
|
Tanc Re complex 3D plot
|
See also
References
- ^ Weisstein, Eric W. "Tanc Function". mathworld.wolfram.com. Retrieved 2022-11-17.