Symbolic differentiation of Bessel functions is incorrect
16 visualizzazioni (ultimi 30 giorni)
Mostra commenti meno recenti
Sam Spedding
il 11 Mar 2021
Commentato: David Goodmanson
il 16 Mag 2022
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?!?
0 Commenti
Risposta accettata
David Goodmanson
il 11 Mar 2021
Modificato: David Goodmanson
il 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)
0 Commenti
Più risposte (1)
Selçuk Sehitoglu
il 15 Mag 2022
Hello,
i am dealing with the same problem for besselj.
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) ans it is undefined at x=0.
However, the answer is available with the following expression:
-(J(n-1,x) - J(n+1,x))/2
Is there a way to use this expression?
Thanks in advance,
Ozi
1 Commento
David Goodmanson
il 16 Mag 2022
Hi Ozi,
Yes there is. The expression works as is. It looks like n = 0 might be an exception because you will need J(-1,x) but for real n the besselj function works for negative n.
Vedere anche
Categorie
Scopri di più su Bessel functions in Help Center e File Exchange
Community Treasure Hunt
Find the treasures in MATLAB Central and discover how the community can help you!
Start Hunting!