A First Course in Complex Analysis · Problem 7.5.34

Taylor and Laurent Series — Beck, Marchesi, Pixton & Sabalka

Mathematics — Complex Analysis · power-series-closed-form

Problem

Find a function representing each of the following series. (a)

\displaystyle\sum_{k\geq 0}\frac{z^{2k}}{k!}

(b)

\displaystyle\sum_{k\geq 1} k\,(z-1)^{k-1}

(c)

\displaystyle\sum_{k\geq 2} k(k-1)\,z^k