- #1
mjordan2nd
- 177
- 1
My textbook states
[tex]
J_v(x) J'_{-v}(x) - J'_v(x) J_{-v}(x) = -\frac{2 \sin v \pi}{\pi x}
[/tex]
My textbook derives this by showing that
[tex]
J_v(x) J'_{-v}(x) - J'_v(x) J_{-v}(x) = \frac{C}{x}
[/tex]
where C is a constant. C is then ascertained by taking x to be very small and using only the first order of the power series expansion for Bessel functions. Does this mean that this computation for C is inexact? It seems that there should be some error terms in there from higher powers of x, or am I missing something?
By the way, I'm using Arfken/Weber and N.N. Lebedev as my guide here.
Thanks for any help.
Edit: Perhaps this would have been better in the differential equations section?
[tex]
J_v(x) J'_{-v}(x) - J'_v(x) J_{-v}(x) = -\frac{2 \sin v \pi}{\pi x}
[/tex]
My textbook derives this by showing that
[tex]
J_v(x) J'_{-v}(x) - J'_v(x) J_{-v}(x) = \frac{C}{x}
[/tex]
where C is a constant. C is then ascertained by taking x to be very small and using only the first order of the power series expansion for Bessel functions. Does this mean that this computation for C is inexact? It seems that there should be some error terms in there from higher powers of x, or am I missing something?
By the way, I'm using Arfken/Weber and N.N. Lebedev as my guide here.
Thanks for any help.
Edit: Perhaps this would have been better in the differential equations section?
Last edited: