/sci/ - Science & Math » Thread #12053143

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Kinna throw this into /sci/ and see what will happen

Anonymous Thu 27 Aug 03:13:54 2020 No.12053143 View Reply Original Report

Quoted By: >>12053185 >>12055943

Function of x, ? and ? are parameters

Anonymous

Anonymous Thu 27 Aug 2020 03:34:15 No.12053185 Report

Quoted By: >>12053188 >>12056486

>>12053143
$(\lambda \text{cos}(\alpha))^{-x}\text{cos}(x \alpha)\Gamma(x)(\text{sec}^2(\alpha))^{-x/2}$ , assuming real numbers

Anonymous

Anonymous Thu 27 Aug 2020 03:37:18 No.12053188 Report

Quoted By: >>12053192

>>12053185
Elaborate?

Anonymous

Anonymous Thu 27 Aug 2020 03:38:23 No.12053192 Report

Quoted By: >>12053199

>>12053188
elaborate on what? that's the result of that integral, assuming the parameters x, alpha, lambda are real numbers.

Anonymous

Anonymous Thu 27 Aug 2020 03:44:50 No.12053199 Report

Quoted By: >>12053203

>>12053192
I mean the solution, sorry.

Anonymous

Anonymous Thu 27 Aug 2020 03:45:47 No.12053203 Report

Quoted By: >>12053208 >>12053577 >>12056486

>>12053199
no, I used Mathematica to solve it. nobody in their right mind would want to solve this by hand.

Anonymous

Anonymous Thu 27 Aug 2020 03:48:32 No.12053208 Report

Quoted By: >>12053258

>>12053203
I think if you expand the cos term into a complex exponential, this turns into two integrals that are both very similar in form to the gamma function, and the work from there is relatively simple.

Anonymous

Anonymous Thu 27 Aug 2020 04:15:52 No.12053258 Report

Quoted By:

>>12053208
There we go, got it! Thanks!

Anonymous

Anonymous Thu 27 Aug 2020 07:14:24 No.12053548 Report

Quoted By:

based classical analysis

> inb4 Mathematica smarter than thou

Anonymous

Anonymous Thu 27 Aug 2020 07:32:36 No.12053577 Report

Quoted By:

>>12053203
This is a well known type of integral that comes up if you wanted to e.g. prove the transformation properties of the theta functions by the residue theorem.

Anonymous

Anonymous Thu 27 Aug 2020 22:50:26 No.12055943 Report

Quoted By:

>>12053143
I'd have to dig up a textbook but it reminds me of one of those integrals for the method of stationary phase or saddle point approximation

Anonymous

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Anonymous Fri 28 Aug 2020 02:59:10 No.12056486 Report

Quoted By: >>12057025 >>12057029 >>12057351 >>12057402 >>12058322

This is the solution you get with and without expressing cosine as the real part of Euler's formula. The resulting integral is just the Bernoulli expression for Gamma.

>>12053185
>>12053203
Fucking trog

Anonymous

Anonymous Fri 28 Aug 2020 08:10:40 No.12057025 Report

Quoted By:

>>12056486

based & saved
ty

Anonymous

Anonymous Fri 28 Aug 2020 08:14:31 No.12057029 Report

Quoted By:

>>12056486
This is good work, son. You make me proud.

Anonymous

Anonymous Fri 28 Aug 2020 11:03:01 No.12057351 Report

Quoted By:

>>12056486
I always felt uneasy with this resolution, particularly with the subsitution of q real variable by a complex variable. It just seems some physicist's "we got that right but dont know why".

Anonymous

Anonymous Fri 28 Aug 2020 11:21:04 No.12057402 Report

Quoted By:

>>12056486
based

Anonymous

Anonymous Fri 28 Aug 2020 17:14:33 No.12058322 Report

Quoted By:

>>12056486
Chad post

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