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/sci/ - Science & Math

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5847923 No.5847923 [Reply] [Original]

How do I do intigrals of infinite products? I know it can't be treated like the intigral of an infinite sum, but are there any similar tricks?

>> No.5847945
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5847945

There is a similar expression in what is known as cluster expansion (in statistical mechanics). One uses graphical representations to get hold of the terms, after some justification that you can collect them in a sum of sums.

Maybe this keyword helps, google it.
Here is the wiki article on it

http://en.wikipedia.org/wiki/Cluster_expansion#Calculation_of_the_configuration_integral

>> No.5847977

<span class="math">\int\prod f_n(x) = \prod\int f_n(x)[/spoiler]

Bro, do you even calculus?

>> No.5847988

>>5847977
20/10

>> No.5847993

maybe your functions are such as you can substitute 1+fn(z)=exp(y)?

>> No.5847995
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5847995

>>5847988
this

>wait wut
>work out simple example
>mfw

>> No.5847997

maybe you should give more details about fn(z)

>> No.5848024

>>5847977
this (replacing one parameter z with two parameters a and b) will, in general, be no simplification of the problem. Of course, all depends on f.

>> No.5848042

>>5847923
I feel like there's something binomial going on here and you could use the pascal triangle to find some general solution, but then that depends on if your subscript on the function there actually denotes different functions of Z.

>> No.5848077

OP here

I will take note of these suggestions.

>>5847945
I'll have to look into that a little more, it is beyond me at the moment.