My textbook states(adsbygoogle = window.adsbygoogle || []).push({});

[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?

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# Wronskian of Bessel Functions of non-integral order v, -v

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