Integration with Bessel function

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Homework Help Overview

The discussion revolves around evaluating an integral involving a Bessel function, specifically J_{3}(\lambda_{m}r), and a function α(r). The integral is presented as part of a larger context related to solving the wave equation in polar coordinates.

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • Participants explore the potential use of recurrence relations for Bessel functions and question the implications of the unspecified function α(r) on the integral's evaluation.

Discussion Status

The discussion is ongoing, with participants raising questions about the nature of α(r) and its impact on the integral. There is no explicit consensus on how to proceed, as the original poster is uncertain whether to leave the integral as is or seek further guidance.

Contextual Notes

The problem context includes a lack of specification for the function α(r), which may influence the approach to the integral. Additionally, there are reminders about adhering to homework guidelines in the discussion.

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I would like to evaluate the following integral which has a Bessel function J_{3}(\lambda_{m}r), and \alpha(r) is a function.

\int^{a}_{0} \alpha(r)rJ_{3}(\lambda_{m}r)dr

I'm unsure how to proceed due to the Bessel function. Am I supposed to use a recurrence relation? Which one?
 
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It depends on what the function α(r) is.
 
The integral is part of a larger problem, which is to solve the wave equation in polar coordinates. The problem statement does not specify α(r).

Should I just leave the integral as is?
 
If this is homework, follow the homework template. We're not here to guess what you should or should no be doing.
 

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