I am solving a problem that in which I got a differential equation of the form $$\sum_{l=0}^{l=\infty}\left[\frac{d^2g_{l}}{dz^2}-\frac{l(l+1)g_{l}}{z(z-1)}\right]p_{l}(cos\theta)=-\frac{2q}{z} \delta(z-a) \delta(cos\theta - 1)$$ Now integration is performed such that from $-a$ to $a$ and the result obtained is $$\left[\frac{dg_{l}}{dz}\right]_{z=-a}^{z=+a}=-\frac{(2l+1)q}{a}$$ I don't know how? I shall be very thank full if if any one will help!
2026-03-27 18:17:36.1774635456
differential equation and its integration
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