A community for students.
Here's the question you clicked on:
 0 viewing
anonymous
 4 years ago
i need help with an integral\[\int x J_n^2(x) \ \text{d}x\]
anonymous
 4 years ago
i need help with an integral\[\int x J_n^2(x) \ \text{d}x\]

This Question is Closed

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0\[J _{n}\] is just any arbitary function ?

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0bessel function of first kind

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0\[x^2\frac{ d^2y }{ dx^2 }+x \frac{ dy }{ dx }+(x^2n^2)y=0\]

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0so the bessel function is the solution to this curve

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0can we find the intergral of these

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0emm...im just trying !! i dont know :(

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0Well 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

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0So 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

anonymous
 4 years ago
Best 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

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0can u show me the steps with wolfram?

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0No, 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

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0dw:1350273811145:dw

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0dw:1350274006370:dw

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0dw:1350274137879:dw

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0dw:1350274335219:dw
Ask your own question
Sign UpFind more explanations on OpenStudy
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.