`cosc`

Compute the cosc(x) function, the derivative of sinc(x), where x expressed in radians.

Returns:

\[\begin{cases} \frac{\cos(\pi x)}{x}-\frac{\sin(\pi x)}{\pi x^2}, & x \ne 0\\ 0, & x=0\\ \end{cases}\]

Base.Math.cosc — Function

cosc(x::T) where {T <: Number} -> float(T)

Compute $\cos(\pi x) / x - \sin(\pi x) / (\pi x^2)$ if $x \neq 0$, and $0$ if $x = 0$. This is the derivative of sinc(x).

Return a T(NaN) if isnan(x).

Methods

julia> methods(cosc, (Any,), [Base, Base.Math, Base.MathConstants, Base.MPFR])# 1 method for generic function "cosc" from Base.Math:
 [1] cosc(x::Number)
     @ special/trig.jl:1106

Examples

Real Numbers

julia> cosc(0)
-0.0

julia> cosc(-0.0)
0.0

julia> cosc(1.0)
-1.0

Complex

julia> cosc(0+0im)
-0.0 + 0.0im

Tips

Extended Inputs

Tech Notes

cosc(::Real): by pure julia
cosc(::BigFloat): by MPFR

Version History

Introduced in Julia v1.0 (2018)