Editing Bessel function (section)

=== Sums with Bessel functions ===
The product of two Bessel functions admits the following sum:
<math display="block">\sum_{\nu=-\infty}^\infty J_\nu(x) J_{n - \nu}(y) = J_{n}(x + y),</math>
<math display="block">\sum_{\nu=-\infty}^\infty J_\nu(x) J_{\nu + n}(y) = J_{n}(y - x).</math>
From these equalities it follows that
<math display="block">\sum_{\nu=-\infty}^\infty J_\nu(x) J_{\nu + n}(x) = \delta_{n, 0}</math>
and as a consequence
<math display="block">\sum_{\nu=-\infty}^\infty J_{\nu}^2(x) = 1. </math>

These sums can be extended to include a term multiplier that is a polynomial function of the index. For example,
<math display="block">\sum_{\nu=-\infty}^\infty \nu J_\nu(x) J_{\nu + n}(x) = \frac{x}{2} \left( \delta_{n, 1} + \delta_{n, -1} \right),</math>
<math display="block">\sum_{\nu=-\infty}^\infty \nu J_{\nu}^2(x) = 0, </math>
<math display="block">\sum_{\nu=-\infty}^\infty \nu^2 J_\nu(x) J_{\nu + n}(x) = \frac{x}{2} \left( \delta_{n, -1} - \delta_{n, 1} \right) + \frac{x^2}{4} \left( \delta_{n, -2} + 2 \delta_{n, 0} + \delta_{n, 2} \right),</math>
<math display="block">\sum_{\nu=-\infty}^\infty \nu^2 J_{\nu}^2(x) = \frac{x^2}{2}. </math>