Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

When finding the coefficients of a Fourier-Bessel series, the Bessel functions satisfies, for $k_1$and $k_2$ both zeroes of $J_n(t)$, the orthogonality relation given by: $$\int_0^1 J_n(k_1r)J_n(k_2r)rdr = 0, (k_1≠k_2)$$ and for $k_1 = k_2 = k$:

$$\int_0^1 J_n^2(kr)rdr = \frac12J_n^{'2}(k)$$

I understand how to get the first result since the Bessel's equation can be interpreted as a Sturm-Liouville problem, but how can I show the second one?

share|improve this question
add comment

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Browse other questions tagged or ask your own question.