@@ -9,10 +9,10 @@ domain of the branch `k = 0` is `[-1/e, Inf]`. For `Complex` `z`, and all `k`, t
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the complex plane.
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```jldoctest
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- julia> lambertw(-1/e , -1)
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+ julia> lambertw(-1/ℯ , -1)
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-1.0
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- julia> lambertw(-1/e , 0)
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+ julia> lambertw(-1/ℯ , 0)
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-1.0
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julia> lambertw(0, 0)
@@ -24,6 +24,10 @@ julia> lambertw(0, -1)
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julia> lambertw(Complex(-10.0, 3.0), 4)
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-0.9274337508660128 + 26.37693445371142im
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```
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+
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+ ```@meta
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+ DocTestSetup = :(using SpecialFunctions)
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+ ```
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"""
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lambertw (z:: Number , k:: Integer = 0 ; maxiter:: Integer = 1000 ) = _lambertw (z, k, maxiter)
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@@ -269,19 +273,23 @@ If `k=-1` and `imag(z) < 0`, the value on the branch `k=1` is returned.
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# Example
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```jldoctest
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- julia> lambertw(-1/e + 1e-18, -1)
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+ julia> lambertw(-1/ℯ + 1e-18, -1)
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-1.0
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julia> lambertwbp(1e-18, -1)
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-2.331643983409312e-9
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# Same result, but 1000 times slower
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- julia> convert(Float64, (lambertw(-BigFloat(1)/e + BigFloat(10)^(-18), -1) + 1))
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+ julia> convert(Float64, (lambertw(-BigFloat(1)/ℯ + BigFloat(10)^(-18), -1) + 1))
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-2.331643983409312e-9
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```
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+ ```@meta
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+ DocTestSetup = :(using SpecialFunctions)
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+ ```
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+
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!!! note
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- `lambertwbp` uses a series expansion about the branch point `z=-1/e ` to avoid loss of precision.
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+ `lambertwbp` uses a series expansion about the branch point `z=-1/ℯ ` to avoid loss of precision.
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The loss of precision in `lambertw` is analogous to the loss of precision
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in computing the `sqrt(1-x)` for `x` close to `1`.
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"""
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