Can we find derivative of bessel functions in matlab directly?

For example if i have x can be any value. I need to know how we can find the derivative directly in MATLAb. for m=0,1.

Answer 1

[Torsten]

You can compute it symbolically first and insert the result as a numerical expression in your code.

syms x
diff(besselj(0,x),x)

ans = 

diff(besselj(1,x),x)

ans = 

Answer 2

[David Goodmanson]

Hi Javeria,

Here is a function that produces J'm(x) for integer m.

function y = besseljd(n,x,opt)

% derivative of bessel function of integer order.
% input s is optional.
% if s = 1, result is scaled by exp(-abs(imag(z))), same as with besselj.
% default is 0, no scaling. 
% note that there is another available expression besides the one used below:
%       y =  besselj(n-1,x,s) - n*besselj(n,x,s)./x; 
%   
% y = besseljd(n,x,s);

if nargin == 3
    s = opt;
else
    s = 0;
end

y = -besselj(n+1,x,s) + n*besselj(n,x,s)./x;

% get rid of nans, integer order
if n==1
    y(x==0) = 1/2;
else
    y(x==0) = 0;
end

[Javeria]

Can we make use of only one line which calculate the derivative of bessel functions just we only switch cases i.e mode m= 0, 1.

[David Goodmanson]

I'm not sure exactly what you mean but if scaling is not needed then the single line

y = -besselj(n+1,x) + n*besselj(n,x)./x;

works unless x = 0. If x = 0 then you still need the four last lines in the code above.