Small approximation of the Derivative of the Bessel function

[KyleS4562]

Hi everyone,

I have an equation that contains the derivative of the Bessel Function of the first kind. I need to evaluate J_n'(x) for small values of x (x<<1). I know that J_n(x) is (x)ⁿ/(2ⁿ*n!). What is it for the derivative?

 

[JJacquelin]

Hi !

You can derivate the series expansion or alternatively expand the formal derivative. Both methods leads to the same result.

 

[KyleS4562]

Thank You!