2
$\begingroup$

If we have a sum of the form $$I = \sum_{k=c}^{\infty} a_k$$ Where both $I$ and $a_k$ are known, is it in general possible to find a closed form solution for $$\sum_{k=c}^{\infty} a_k z^k$$

  • 0
    Let's see: $\sum_{k \geq 1} 1/k^2 = \pi^2/6$ and $\sum_{k \geq 1} 1/k^4 = \pi^4/90$. Do $\sum_{k \geq 1} z^k/k^2$ and $\sum_{k \geq 1} z^k/k^4$ have a closed form? – 2017-02-17
  • 0
    Not unless you count the polylogarithm to be closed form. – 2017-02-17
  • 1
    That's why I gave the second example. You can keep making up names for functions you don't already have a name for, but that seems to defeat the point of the vague term "closed form". – 2017-02-17

0 Answers 0