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/sci/ - Science & Math

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4569458 No.4569458 [Reply] [Original]

Are the gamma function and the beta function important?
I saw some proofs about how different representations of them are equivalent.
Is that shit worth memorizing? Where do you need these functions?

inb4 wikipedia: I read the article, it's not helpful.

>> No.4569466

You need them in stochastic.

>> No.4569468
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4569468

http://en.wikipedia.org/wiki/Gamma_function
http://en.wikipedia.org/wiki/Beta_function

>> No.4569482

>>4569466
Where? What properties of them are useful to model real world phenomena?

>> No.4569494

>>4569482
http://en.wikipedia.org/wiki/Gamma_distribution
http://en.wikipedia.org/wiki/Beta_distribution

>> No.4569504

They appear in many solutions of differential equations which are expressed as an infinite series since it extends the factorial function to non integers. An example would be the Bessel functions as a solution to the motion of your coffee when you spin the cup

>> No.4569508

>>4569494
>>4569504
Well thanks. Looks like I'll need a lot more of higher math knowledge for understanding and applying those. I just came across them in an analysis book where they are introduced and some properties are proven without any hint on applications.

>> No.4569937

yes, they are good for generalizing recursively defined ODEs, but they also show up in probability and statistics, and the gamma constant that derives from it shows up in a lot of places like prime counting and the zeta function

there is a book "gamma: exploring euler's constant" which gives a rigorous overview of where the gamma constant and function show up