File:Gamma function.gif
Summary
| Description |
English: The Gamma function has the property that if you multiply it by x, you are effectively just shifting it by 1.
It is not the only function with this property, but in a sense it is the "nicest" one. |
| Date | |
| Source | https://twitter.com/j_bertolotti/status/1375122099275202567 |
| Author | Jacopo Bertolotti |
| Permission (Reusing this file) |
https://twitter.com/j_bertolotti/status/1030470604418428929 |
Mathematica 12.0 code
sinstep[t_] := Sin[\[Pi]/2 t]^2
frames1 = Table[
Plot[{sinstep[t] (x - 1) + 1, Gamma[x], (sinstep[t] (x - 1) + 1) Gamma[x]}, {x, -5, 5}, PlotRange -> {-10, 10}, PlotStyle -> {Directive[Dashed, Gray], Directive[LightGray], Directive[Thick, Black]}, PlotLabel -> "x \[CapitalGamma](x) = \[CapitalGamma](x+1)", LabelStyle -> {Black, Bold}, TicksStyle -> Directive[Gray, 10] ]
, {t, 0, 1, 0.025}];
frames2 = Table[
Plot[{x - sinstep[t], Gamma[x], (x - sinstep[t]) Gamma[x - sinstep[t]]}, {x, -5, 5}, PlotRange -> {-10, 10}, PlotStyle -> {Directive[Dashed, Gray], Directive[LightGray], Directive[Thick, Black]}, PlotLabel -> "x \[CapitalGamma](x) = \[CapitalGamma](x+1)", LabelStyle -> {Black, Bold}, TicksStyle -> Directive[Gray, 10]]
, {t, 0, 1, 0.025}];
ListAnimate[Join[frames1, frames2]]
Licensing
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This file is made available under the Creative Commons CC0 1.0 Universal Public Domain Dedication. |
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