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mukushla
Group Title
i need help with an integral\[\int x J_n^2(x) \ \text{d}x\]
 one year ago
 one year ago
mukushla Group Title
i need help with an integral\[\int x J_n^2(x) \ \text{d}x\]
 one year ago
 one year ago

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mukushla Group TitleBest ResponseYou've already chosen the best response.0
@mahmit2012
 one year ago

Jonask Group TitleBest ResponseYou've already chosen the best response.0
\[J _{n}\] is just any arbitary function ?
 one year ago

mukushla Group TitleBest ResponseYou've already chosen the best response.0
bessel function of first kind
 one year ago

Jonask Group TitleBest ResponseYou've already chosen the best response.0
i am out then
 one year ago

Jonask Group TitleBest ResponseYou've already chosen the best response.0
\[x^2\frac{ d^2y }{ dx^2 }+x \frac{ dy }{ dx }+(x^2n^2)y=0\]
 one year ago

Jonask Group TitleBest ResponseYou've already chosen the best response.0
so the bessel function is the solution to this curve
 one year ago

Jonask Group TitleBest ResponseYou've already chosen the best response.0
can we find the intergral of these
 one year ago

mukushla Group TitleBest ResponseYou've already chosen the best response.0
emm...im just trying !! i dont know :(
 one year ago

vf321 Group TitleBest ResponseYou've already chosen the best response.0
Well my good friend wikipedia tells us that we can expand the Bessel Function as follows with taylor series: http://upload.wikimedia.org/math/1/b/2/1b23400208b273377e8cdec7d82f0242.png
 one year ago

vf321 Group TitleBest ResponseYou've already chosen the best response.0
So then the integral becomes: \[\int x\sum_{m=0}^\infty \frac{(1)^m}{m!(m+n)!}(\frac{1}{2}x)^{2m+n}\]for integer orders
 one year ago

vf321 Group TitleBest ResponseYou've already chosen the best response.0
\[\int x\left(\sum_{m=0}^\infty \frac{(1)^m}{m!(m+n)!}(\frac{1}{2}x)^{2m+n}\right)^2 dx\]  forgot the dx
 one year ago

mukushla Group TitleBest ResponseYou've already chosen the best response.0
can u show me the steps with wolfram?
 one year ago

vf321 Group TitleBest ResponseYou've already chosen the best response.0
No, I can't. But you do see the answer, right? My guess is that to get the answer you have to write \((\sum...)^2\) as a single sum using binomial expansion or something, then you can integrate it easily since it's just a polynomial. Then you reconstruct the sum as three separate sums and get the nice answer that alpha got: http://www.wolframalpha.com/input/?i=integrate+x+BesselJ[n%2C+x]^2+dx
 one year ago

mahmit2012 Group TitleBest ResponseYou've already chosen the best response.2
dw:1350273811145:dw
 one year ago

mahmit2012 Group TitleBest ResponseYou've already chosen the best response.2
dw:1350274006370:dw
 one year ago

mahmit2012 Group TitleBest ResponseYou've already chosen the best response.2
dw:1350274137879:dw
 one year ago

mahmit2012 Group TitleBest ResponseYou've already chosen the best response.2
dw:1350274335219:dw
 one year ago
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