# Problem with ImplicitEquation involving the incomplete gamma function

**URL:** <https://discourse.julialang.org/t/problem-with-implicitequation-involving-the-incomplete-gamma-function/84247>\
**Category:** Numerics\
**Tags:** question, plotting\
**Created:** [July 14, 2022, 10:42pm UTC](https://discourse.julialang.org/t/problem-with-implicitequation-involving-the-incomplete-gamma-function/84247 "2022-07-14T22:42:19Z")\
**Posts on this page:** 3\
**Page:** 1

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**Author:** ![Dennis-Yang87](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/dennis-yang87/32/37967_2.png) [@Dennis-Yang87](https://discourse.julialang.org/u/Dennis-Yang87)\
**Post date:** [July 14, 2022, 10:42pm UTC](https://discourse.julialang.org/t/problem-with-implicitequation-involving-the-incomplete-gamma-function/84247/1 "2022-07-14T22:42:19Z")

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Hi everyone,

I am new to Julia and trying to plot an implicit function involving [incomplete gamma function Q(x, a)](https://specialfunctions.juliamath.org/stable/functions_list/#SpecialFunctions.gamma_inc) with the code below (gamma\_inc returns a two-element tuple and I only need the second element, so the index [2] is used)

```julia
using SpecialFunctions
using Plots, ImplicitEquations 

f(phi, z) = z*gamma_inc((floor(1/phi) - 1), z)[2]
plot(f ⩵ 1; xlims = (0,0.26), ylims = (0, 16))

```

however it keeps giving the following error messages:

```julia
MethodError: no method matching _gamma_inc(::ImplicitEquations.OInterval, ::ImplicitEquations.OInterval, ::Int64)
Closest candidates are:
  _gamma_inc(::Float64, ::Float64, ::Integer) at C:\Users\.julia\packages\SpecialFunctions\FhmL1\src\gamma_inc.jl:860
  _gamma_inc(::BigFloat, ::BigFloat, ::Integer) at C:\Users\.julia\packages\SpecialFunctions\FhmL1\src\gamma_inc.jl:950
  _gamma_inc(::Float32, ::Float32, ::Integer) at C:\Users\.julia\packages\SpecialFunctions\FhmL1\src\gamma_inc.jl:956
  ...

```

Does this imply that the gamma\_inc function (from the SpecialFunctions package) doesn’t work with ImplicitEquations? Thanks.

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<div class="post-metadata">

**Author:** ![j\_verzani](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/j_verzani/32/8551_2.png) [@j\_verzani](https://discourse.julialang.org/u/j_verzani)\
**Post date:** [July 15, 2022, 12:25am UTC](https://discourse.julialang.org/t/problem-with-implicitequation-involving-the-incomplete-gamma-function/84247/2 "2022-07-15T00:25:10Z")

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Try [GitHub - saschatimme/ImplicitPlots.jl: Julia package for the plotting of plane curves and surfaces](https://github.com/saschatimme/ImplicitPlots.jl) which doesn’t use interval arithmetic. It is faster too. There is also IntervalConstraintProgramming.jl

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<div class="post-metadata">

**Author:** ![Dennis-Yang87](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/dennis-yang87/32/37967_2.png) [@Dennis-Yang87](https://discourse.julialang.org/u/Dennis-Yang87)\
**Post date:** [July 15, 2022, 1:45am UTC](https://discourse.julialang.org/t/problem-with-implicitequation-involving-the-incomplete-gamma-function/84247/3 "2022-07-15T01:45:38Z")

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Thank you! I’ll try them.