@@ -8,11 +8,11 @@ either `0` or `-1`. For `Real` `z`, the domain of the branch `k = -1` is `[-1/e,
8
8
domain of the branch `k = 0` is `[-1/e, Inf]`. For `Complex` `z`, and all `k`, the domain is
9
9
the complex plane.
10
10
11
- ```jldoctest
12
- julia> lambertw(-1/e , -1)
11
+ ```jldoctest; setup=:(using SpecialFunctions)
12
+ julia> lambertw(-1/ℯ , -1)
13
13
-1.0
14
14
15
- julia> lambertw(-1/e , 0)
15
+ julia> lambertw(-1/ℯ , 0)
16
16
-1.0
17
17
18
18
julia> lambertw(0, 0)
@@ -268,20 +268,19 @@ The result is accurate to Float64 precision for abs(z) < 0.32.
268
268
If `k=-1` and `imag(z) < 0`, the value on the branch `k=1` is returned.
269
269
270
270
# Example
271
- ```jldoctest
272
- julia> lambertw(-1/e + 1e-18, -1)
271
+ ```jldoctest; setup=:(using SpecialFunctions)
272
+ julia> lambertw(-1/ℯ + 1e-18, -1)
273
273
-1.0
274
274
275
275
julia> lambertwbp(1e-18, -1)
276
276
-2.331643983409312e-9
277
277
278
- # Same result, but 1000 times slower
279
- julia> convert(Float64, (lambertw(-BigFloat(1)/e + BigFloat(10)^(-18), -1) + 1))
278
+ julia> convert(Float64, (lambertw(-big(1)/ℯ + big(10)^(-18), -1) + 1)) # Same result, but 1000 times slower
280
279
-2.331643983409312e-9
281
280
```
282
281
283
282
!!! note
284
- `lambertwbp` uses a series expansion about the branch point `z=-1/e ` to avoid loss of precision.
283
+ `lambertwbp` uses a series expansion about the branch point `z=-1/ℯ ` to avoid loss of precision.
285
284
The loss of precision in `lambertw` is analogous to the loss of precision
286
285
in computing the `sqrt(1-x)` for `x` close to `1`.
287
286
"""
0 commit comments