Okay, for the first one is it the case that x is valid over the interval \left[0<x<\frac{\pi}{2}\right], therefore z is valid over the same interval? That seems to solve my problem with the maths.
For the second boundary case would it be that it is equally possible to say A = B = 0 as it is...
Use Green's Functions to solve:
\frac{d^{2}y}{dx^{2}} + y = cosec x
Subject to the boundary conditions:
y\left(0\right) = y\left(\frac{\pi}{2}\right) = 0
Attempt:
\frac{d^{2}G\left(x,z\right)}{dx^{2}} + G\left(x,z\right) = \delta\left(x-z\right)
For x\neq z the RHS is zero...
1. The problem statement:
Show that the following series has a radius of convergence equal to exp\left(-p\right)
Homework Equations
For p real:
\Sigma^{n=\infty}_{n=1}\left( \frac{n+p}{n}\right)^{n^{2}} z^{n}
The Attempt at a Solution...