@@ -9,10 +9,10 @@ domain of the branch `k = 0` is `[-1/e, Inf]`. For `Complex` `z`, and all `k`, t
99the complex plane.
1010
1111```jldoctest
12- julia> lambertw(-1/e , -1)
12+ julia> lambertw(-1/ℯ , -1)
1313-1.0
1414
15- julia> lambertw(-1/e , 0)
15+ julia> lambertw(-1/ℯ , 0)
1616-1.0
1717
1818julia> lambertw(0, 0)
@@ -24,6 +24,10 @@ julia> lambertw(0, -1)
2424julia> lambertw(Complex(-10.0, 3.0), 4)
2525-0.9274337508660128 + 26.37693445371142im
2626```
27+
28+ ```@meta
29+ DocTestSetup = :(using SpecialFunctions)
30+ ```
2731"""
2832lambertw (z:: Number , k:: Integer = 0 ; maxiter:: Integer = 1000 ) = _lambertw (z, k, maxiter)
2933
@@ -269,19 +273,23 @@ If `k=-1` and `imag(z) < 0`, the value on the branch `k=1` is returned.
269273
270274# Example
271275```jldoctest
272- julia> lambertw(-1/e + 1e-18, -1)
276+ julia> lambertw(-1/ℯ + 1e-18, -1)
273277-1.0
274278
275279julia> lambertwbp(1e-18, -1)
276280-2.331643983409312e-9
277281
278282# Same result, but 1000 times slower
279- julia> convert(Float64, (lambertw(-BigFloat(1)/e + BigFloat(10)^(-18), -1) + 1))
283+ julia> convert(Float64, (lambertw(-BigFloat(1)/ℯ + BigFloat(10)^(-18), -1) + 1))
280284-2.331643983409312e-9
281285```
282286
287+ ```@meta
288+ DocTestSetup = :(using SpecialFunctions)
289+ ```
290+
283291!!! note
284- `lambertwbp` uses a series expansion about the branch point `z=-1/e ` to avoid loss of precision.
292+ `lambertwbp` uses a series expansion about the branch point `z=-1/ℯ ` to avoid loss of precision.
285293 The loss of precision in `lambertw` is analogous to the loss of precision
286294 in computing the `sqrt(1-x)` for `x` close to `1`.
287295"""
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