Bessel's Equation and Rodrique Formula

[Sudip Pradhan]

Is there any relation between Rodrique formula and Bessel's equation? Is it necessary to apply Rodrigue formula in the Bessel's Equation?

 

[fzero]

I do not believe that there is a Rodrigues-type formula for the Bessel functions, since there is no representation of a Bessel function in terms of a polynomial of finite order. The Taylor series representations are infinite series. There is a slightly different type of presentation called a generating function that can be used to express the Bessel functions in terms of derivatives of an elementary function. See sect. 2.1 of http://www.math.psu.edu/papikian/Kreh.pdf for some details.