Add examples to series() and taylor() docstrings

Author: hersle

src/taylor.jl

@@ -2,6 +2,19 @@
     series(y, x, [x0=0,] ns; name = nameof(y))
 
 Expand the variable `y` in a power series in the variable `x` around `x0` to orders `ns`.
+
+Examples
+========
+
+```julia
+julia> @variables z ϵ
+2-element Vector{Num}:
+ z
+ ϵ
+
+julia> series(z, ϵ, 2, 0:3)
+z[0] + z[1]*(-2 + ϵ) + z[2]*((-2 + ϵ)^2) + z[3]*((-2 + ϵ)^3)
+```
 """
 function series(y, x, x0, ns; name = nameof(y))
     c, = @variables $name[ns]
@@ -15,6 +28,21 @@ end
     taylor_coeff(f, x[, n]; rationalize=true)
 
 Calculate the `n`-th order coefficient(s) in the Taylor series of `f` around `x = 0`.
+
+Examples
+========
+```julia
+julia> @variables x y
+2-element Vector{Num}:
+ x
+ y
+
+julia> taylor_coeff(series(y, x, 0:5), x, 0:2:4)
+3-element Vector{Num}:
+ y[0]
+ y[2]
+ y[4]
+```
 """
 function taylor_coeff(f, x, n = missing; rationalize=true)
     if n isa AbstractArray
@@ -70,6 +98,9 @@ julia> taylor(exp(x), x, 0:3; rationalize=false)
 
 julia> taylor(√(x), x, 1, 0:3)
 1 + (1//2)*(-1 + x) - (1//8)*((-1 + x)^2) + (1//16)*((-1 + x)^3)
+
+julia> isequal(taylor(exp(im*x), x, 0:5), taylor(exp(im*x), x, 0:5))
+true
 ```
 """
 function taylor(f, x, ns; kwargs...)