Integral of first order (first kind) bessel function

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SUMMARY

The integral of the first order Bessel function J1(kR) from zero to infinity has an analytical solution, which is 1/R. The discussion highlights the properties of Bessel functions, noting that their anti-derivatives can also be expressed as Bessel functions. Additionally, the asymptotic behavior of these functions is crucial for understanding the integration process, particularly when dealing with limits of zero and infinity.

PREREQUISITES
  • Understanding of Bessel functions, specifically J1(kR)
  • Knowledge of integral calculus and limits
  • Familiarity with analytical and numerical integration techniques
  • Basic properties of asymptotic behavior in mathematical functions
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  • Study the properties of Bessel functions and their applications in physics
  • Learn about numerical integration methods for functions with infinite limits
  • Explore asymptotic analysis in mathematical functions
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Mathematicians, physicists, and engineers who work with Bessel functions and require a deeper understanding of their integrals and properties.

Pratyush
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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.
 
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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 ...
 
hey thanks a lot...

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

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