# Two Bessel Integrarion problem

1. Nov 25, 2008

### hongjs

I am calculating the Poynting Vector along a circular waveguide (a simplest circular waveguide which only contains a dielectric medium inside and is coverd by perfect conductor).

When calculating this, two Bessel function integration appear which state:

1. ∫ {Jn'[(tnl/a)r]}^2 rdr, in [0, a]

2. ∫ {Jn[(tnl/a)r]}^2/r dr, in [0, a]

where a is the circular waveguide radius, tnl is the lth rooth of the nth-order Bessel function, Jn denotes Bessel function of the first kind, Jn' denotes first order differential of Jn

Is there any one that knows how to solve these two integration?

Thank you in advance!

ps. If the formula is not clear, please see the attached picture

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