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!!!

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KyleS4562	Small approximation of the Derivative of the Bessel function 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. Attached Thumbnails