# How can I evaluate the derivatives of a Bessel function at different points?

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MathWorks Support Team on 27 Jun 2009
Answered: Md Rezaul Karim on 19 Apr 2020
I would like to evaluate the derivatives of Bessel function, I would like to know if I can do this in MATLAB.

MathWorks Support Team on 27 Jun 2009
There is no direct function to calculate the value of the derivatives of a Bessel Function, however, one can use the following identity to get it:
J(s-1)(z) - J(s+1)(z) = 2J'(s)(z)
where s, s-1 and s+1 are the orders of the Bessel function and z is the point of evaluation. One can use similar identities for Hankel functions.

Song Wang on 20 Mar 2019
Taking
dJ = -besselj(1, z)

ANDONI PULIDO on 2 Dec 2019
Edited: ANDONI PULIDO on 2 Dec 2019
Use Matlab to obtain the derivative of your funktion:
>> syms z;
f=besseli(0,z*sqrt(1*i));
g=diff(f,z);
>> g
g = 2^(1/2)*besseli(1, 2^(1/2)*z*(1/2 + 1i/2))*(1/2 + 1i/2)
Best regards

Md Rezaul Karim on 19 Apr 2020
the derivatives of Bessel function:
% *J = besselj(nu,Z,scale)*
% *scale* - 0(default) or 1
% *Z* - Normalized kc by inner or outer radii of cable
% *n* - The order of the bessel function.
% taking differentiation J'_n(z)=(n/z)*J_n(z)-J_(n+1)(z)

Md Rezaul Karim on 19 Apr 2020
syms x;
diff(bessely(1, x))= bessely(0, x) - bessely(1, x)/x;

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