Recent content by aamir.ahmed

Consider the multipole expansion of Newtonian potential 1/R in 2D in terms of Legendre functions. \begin{align} \mathbf{r_1} &= (r , \theta_1) \\ \mathbf{r} &= (r , \theta) \\ \phi(\mathbf{r}-\mathbf{r_1}) &= \frac{1}{\left|\mathbf{r}-\mathbf{r_1}\right|} \\...

Hi, I need help to determine the upper bound of this infinite series. \sum_{k=p+1}^{\infty} \frac{1}{k} a^k \ \ \ \ ; a \leq 1 The paper I am reading reports the upper bound to be, \sum_{k=p+1}^{\infty} \frac{1}{k} a^k \leq \frac{1}{p+1}\sum_{k=p+1}^{\infty} a^k = \frac{1}{p+1} \cdot...