File:Gamma property.gif
Gamma_property.gif (600 × 250 pixels, file size: 719 KB, MIME type: image/gif, looped, 160 frames, 5.3 s)
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Summary
editDescriptionGamma property.gif |
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
editusing 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
editI, 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.
http://creativecommons.org/publicdomain/zero/1.0/deed.enCC0Creative Commons Zero, Public Domain Dedicationfalsefalse |
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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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