Derivative of Bessel Function of Second Kind, Zero Order

Question

The derivative of Bessel function of first kind (zero order, $J'_0$) is $-J_1$. What is the derivative of Bessel function of second kind (zero order, $Y'_0$)?

I could find $I'_0$ and $K'_0$, but not $Y'_0$.

Thanks in advance!

Answer 1

These derivatives are really easy to memorize

$$\frac d {dx}I_0(x)=+I_1(x)$$ $$\frac d {dx}J_0(x)=-J_1(x)$$ $$\frac d {dx}Y_0(x)=-Y_1(x)$$ $$\frac d {dx}K_0(x)=-K_1(x)$$

Now, for higher orders $$\frac d {dx}I_n(x)=+\frac{1}{2} (I_{n-1}(x)+I_{n+1}(x))$$ $$\frac d {dx}J_n(x)=+\frac{1}{2} (J_{n-1}(x)-J_{n+1}(x))$$ $$\frac d {dx}Y_n(x)=+\frac{1}{2} (Y_{n-1}(x)-Y_{n+1}(x))$$ $$\frac d {dx}K_n(x)=-\frac{1}{2} (K_{n-1}(x)+K_{n+1}(x))$$