Application of Bessel Function I have read number of books and online literature on Bessel function. Theoretically, I have known about Bessel function. What is practical significance of Bessel function? How can Bessel function practically interpreted?              
 A: For just one example in probability: consider a football match (soccer for North Americans).  A fairly reasonable model is that each team, independently, scores goals according to a Poisson process.  The expression for the probability that the score is tied after 90 minutes of play involves the modified Bessel function
$I_0$.  
A: $J_1$ is the Bessel function of the first order and it is used for example to model the blur in an image due to an out of focus lens, this modeling is important to restore, or deblur, an out of focus image.
See Image restoration with known degradation by Václav Hlaváč or BIEMOND, Jan; LAGENDIJK, Reginald L.; MERSEREAU, Russell M. Iterative methods for image deblurring. Proceedings of the IEEE, 1990, 78.5: 856-883.
A: For me the most beautiful example of Bessel functions application is to show the vibration modes of a circular membrane. The ways in that a common drum can move and generate sound, various of these modes can be combinated and they have circular and radial components. 

They are also related to the famous Chladni Figures
