Integral of first order (first kind) bessel function

[Pratyush]

hello,

while working on a problem i encountered the following integral :(limits are zero and infinity)

Integral[J1(kR)dk]

J1 is the first order bessel function..cudnt put 1 in subscripts..

Is there an analytical solution for this?? also is it possible to integrate it numerically?

please help. thanks.

 

[Pere Callahan]

The answer is 1/R.

Check some basic properties of Bessel function, you will see that anti-derivatives of Bessel function can be expressed again as Bessel functions, then you have to study the asymptotic behavior of those ...

 

[Pratyush]

hey thanks a lot...

i got daunted by the zero and the infinity...been long since i saw bessel functions...thanks