Attempting to construct a generating function

Generator · **Joined:** Sun, 31 Jan 2010 05:07:26 UTC **Posts:** 88

Consider the following function:

$f(x) = \sum_{i=0}^M{\sum_{j=0}^N{c_i a^{i*j}}x^i}$$

Is it possible to construct such a (generating) function in a simple arithmetic way - meaning that it's possible to make out of addition, subtraction, multiplication, and division only.

In other words, I would like to construct a function like:

$f(x) = \sum_{i=0}^M{a^i}c_0 + \sum_{i=0}^M{a^{2i}}c_1 x + \sum_{i=0}^M{a^{3i}}c_2 x^2 + \dots$

S.O.S. Mathematics CyberBoard

Attempting to construct a generating function

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