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Symbolic differentiation of Bessel functions is incorrect

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Sam Spedding
Sam Spedding 2021 年 3 月 11 日
編集済み: David Goodmanson 2021 年 3 月 11 日
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?!?

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David Goodmanson
David Goodmanson 2021 年 3 月 11 日
編集済み: David Goodmanson 2021 年 3 月 11 日
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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