# How to work around this error in expint?

**URL:** https://discourse.julialang.org/t/how-to-work-around-this-error-in-expint/76133
**Category:** Numerics
**Tags:** specialfunctions
**Created:** [February 10, 2022, 12:31am UTC](https://discourse.julialang.org/t/how-to-work-around-this-error-in-expint/76133 "2022-02-10T00:31:22Z")
**Posts on this page:** 2
**Page:** 1

<div class="post-metadata">

### Author: ![amrods](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/amrods/32/2543_2.png) [@amrods](https://discourse.julialang.org/u/amrods)
#### Post date: [February 10, 2022, 12:31am UTC](https://discourse.julialang.org/t/how-to-work-around-this-error-in-expint/76133/1 "2022-02-10T00:31:22Z")

</div>

I ran into this error while evaluating the Gamma function from `SpecialFunctions`:

```julia
julia> using SpecialFunctions

julia> gamma(exp(19.39)+1, 0.0125*0.6)
ERROR: ArgumentError: Unsupported order |ν| > 50 off the positive real axis
Stacktrace:
 [1] _expint(ν::Float64, z::Float64, niter::Int64, ::Val{false})
   @ SpecialFunctions ~/.julia/packages/SpecialFunctions/9pXme/src/expint.jl:400
 [2] expint (repeats 2 times)
   @ ~/.julia/packages/SpecialFunctions/9pXme/src/expint.jl:516 [inlined]
 [3] _gamma(a::Float64, x::Float64)
   @ SpecialFunctions ~/.julia/packages/SpecialFunctions/9pXme/src/gamma_inc.jl:1059
 [4] gamma(a::Float64, x::Float64)
   @ SpecialFunctions ~/.julia/packages/SpecialFunctions/9pXme/src/gamma_inc.jl:1036
 [5] top-level scope
   @ REPL[43]:1

```

I traced it to this evaluation of `expint`

```julia
julia> expint(1-(exp(19.39)+1), 0.0125*0.6)
ERROR: ArgumentError: Unsupported order |ν| > 50 off the positive real axis
Stacktrace:
 [1] _expint(ν::Float64, z::Float64, niter::Int64, ::Val{false})
   @ SpecialFunctions ~/.julia/packages/SpecialFunctions/9pXme/src/expint.jl:400
 [2] expint (repeats 2 times)
   @ ~/.julia/packages/SpecialFunctions/9pXme/src/expint.jl:516 [inlined]
 [3] top-level scope
   @ REPL[41]:1

```

which in turn arises from this definition of `_expint`:

```julia
function _expint(ν::Number, z::Number, niter::Int=1000, ::Val{expscaled}=Val{false}()) where {expscaled}
    if abs(ν) > 50 && !(isreal(ν) && real(ν) > 0)
        throw(ArgumentError("Unsupported order |ν| > 50 off the positive real axis"))
    end
# rest of code here
end

```

How can I work around this?

---

<div class="post-metadata">

### Author: ![bertschi](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/bertschi/32/33462_2.png) [@bertschi](https://discourse.julialang.org/u/bertschi)
#### Post date: [February 11, 2022, 8:28pm UTC](https://discourse.julialang.org/t/how-to-work-around-this-error-in-expint/76133/2 "2022-02-11T20:28:16Z")

</div>

According to the documentation gamma(a, x) computes the upper incomplete gamma function.  
SpecialFunctions also provides gamma\_inc(a, x) which computes the ratios of the lower and upper incomplete gamma(a, x) functions divided by gamma(a) and returns a tuple of both values.  
Thus, you can compute your function as

```julia
mygamma(a, x) = gamma_inc(a, x)[2] * gamma(a)

```

For your arguments the result is just the same as gamma(exp(19.39) + 1) and way larger than floatmax(Float64). You get a meaningful result on the log scale though:

```julia
logmygamma(a, x) = log(gamma_inc(a, x)[2]) + loggamma(a)

```

julia\> logmygamma(exp(19.39)+1, 0.0125\*0.6)  
4.847878583807443e9