File:Gamma property.gif
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Gamma_property.gif (600 × 250 pixels, file size: 719 KB, MIME type: image/gif, looped, 160 frames, 5.3 s)
Captions
Captions
Showing the link between Gamma(x+1) = xGamma(x), and Gamma(x)
Summary[edit]
| Description |
English: A linear ramp (1+s(x-1))Gamma(x) for 0<s<1, transforms Gamma(x) to Gamma(x+1)=xGamma(x), which is then returned to Gamma(x) by translation. |
| Date | |
| Source | Own work |
| Author | Ashton Bradley |
Julia 1.6 code[edit]
using SpecialFunctions, Plots, LaTeXStrings
gr(grid=false,legend=false,size=(600,250),ylims=(-3,3))
## functions
fp(x) = gamma(x) > 0.0 ? gamma(x) : NaN
fn(x) = gamma(x) < 0.0 ? gamma(x) : NaN
g(x,s) = 1+s*(x-1) # linear ramp
gp(x,s) = g(x,s)*fp(x)
gn(x,s) = g(x,s)*fn(x)
## arrays
x = LinRange(-5.01,5.01,999)
svals = LinRange(0,0.999999,400)
xvals = LinRange(0,0.99899,400)
xa=[zero.(svals);xvals]
sa=[svals;svals[end]*one.(xvals)]
## animate
anim = @animate for (xa,sa) in zip(xa,sa)
plot(x,[gp.(x .-xa,sa),gn.(x .-xa,sa)],line=(:blue,3,0.5))
plot!(x,[fp.(x .+1),fn.(x .+1)],line=(:green,1,0.4))
plot!(x,[fp.(x),fn.(x)],line=(:red,1,0.4))
annotate!(3.7,2.3,L"\Gamma(x)",fontsize=10)
annotate!(1.5,2.3,L"x\Gamma(x)",fontsize=10)
xlabel!(L"x")
end every 5
gif(anim,"gamma.gif",fps=30)
Licensing[edit]
I, the copyright holder of this work, hereby publish it under the following license:
 
|
This file is made available under the Creative Commons CC0 1.0 Universal Public Domain Dedication. |
| The person who associated a work with this deed has dedicated the work to the public domain by waiving all of their rights to the work worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law. You can copy, modify, distribute and perform the work, even for commercial purposes, all without asking permission.
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File history
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| Date/Time | Thumbnail | Dimensions | User | Comment | |
|---|---|---|---|---|---|
| current | 20:25, 6 June 2021 | | 600 × 250 (719 KB) | Yeldarbnothsa (talk | contribs) | Uploaded own work with UploadWizard |
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