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Symbolic differentiation of Bessel functions is incorrect

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The output of the below code gives an incorrect equation for the derivative of the modified Bessel function of the second kind.
syms x n
y = besselk(n,x);
diff(y,x)
It says the derivative of is
but as I understand, the formula for the derivative of the K bessel functions is given by
.
What's going on?!?

Accepted Answer

David Goodmanson
David Goodmanson on 11 Mar 2021
Edited: David Goodmanson on 11 Mar 2021
Hi Sam,
There is really nothing going on. Both of those identities are correct, as you can check numerically. There are several recurrence relations available for Bessel functions. Another one is
K'(n,x) = -nK(n,x)/x - K(n-1,x)

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