Derivative of Bessel function at x=0.

Hello everyone,

I would like to change the expression of derivative of besselj function, because embedded expression is leading some problems.

syms nu x
y=besselj(nu,x);
d_y=diff(y,x);
subs(d_y,x,0); % At this row i get "Division by zero." error, because derivative is defined as -nJ(n,x)/x - J(n-1,x) in MATLAB and it is undefined at x=0.

However, the answer is available with the following expression (mathematically):

-(besselj(n-1,x) - besselj(n+1,x))/2

Is there a way to use this expression?

Thanks in advance,

Ozi

Answer 1

[Star Strider]

One option is to use the limit function, however tha does not always produce a numeric result.

I ususally cheat and use eps instead.

syms nu x 
y(x) = besselj(nu,x);
d_y = diff(y,x)

d_y(x) = 

d_y0 = limit(d_y,x,0)

d_y0 = 

d_y0 = d_y(eps) % Cheat With 'eps'

d_y0 = 

d_y0 = vpa(d_y0)

d_y0 = 

Since ν is undefined, a double result is not possible.

.

[Selçuk Sehitoglu]

Thanks a lot !!!

[Star Strider]

As always, my pleasure!