Dose anyone know about the formulations of derivative of Bessel and Hankel function as below, because when I just used the derivative of Bessel function and Hankel function as in the following references
https://www.boost.org/doc/libs/1_57_0/libs/math/doc/html/math_toolkit/bessel/bessel_derivatives.html
http://mathworld.wolfram.com/HankelFunctionoftheSecondKind.html
Derivative of Bessel function: \begin{align} \text{J}_n^{\prime}(z) &= -\text{J}_{n+1}(z) + \frac{n}{2}\text{J}_n(z). \end{align} Derivative of Hankel function: \begin{align} \text{H}_n^{(2)\prime}(z) &= -\text{H}_{n+1}^{(2)\prime}(z) + \frac{n}{2}\text{H}_n^{(2)\prime}(z). \end{align} Thank you so much!