Derivative of Bessel Function of Second Kind, Zero Order

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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!

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1 Answer

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

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