Mathematical Science & Technologies » Mathematics-Technical

Finite Summation of Integer Powers (Part 3)

Assad Ebrahim — Fri, 02 Apr 2010 10:41:39 +0000

(Discrete Mathematics Techniques III)

Abstract We find a direct closed-form solution, i.e. one that does not require iteration, for the general case of the finite-summation-of-integer-powers problem . Having established in Part 2 that the closed-form solution is a polynomial, the summation is here rewritten as the sum of the independent monomials (), where the [...]

Why Zero Raised to the Zero Power IS One

Assad Ebrahim — Thu, 25 Feb 2010 13:56:16 +0000

The question of what value 0^0 should evaluate to has been discussed since the time of Euler (1700s). There are three candidate choices: 1,0, or “indeterminate” (i.e., throw an error).

In this article, I argue that the only reasonable choice (for discrete mathematics) is 0^0=1 (), and I’ll give a tangible, feel-the-grit-in-your-palms reason [...]

Finite Summation of Integer Powers (Part 2)

Assad Ebrahim — Mon, 08 Feb 2010 19:57:14 +0000

(Discrete Mathematics Techniques II)

Abstract We solve the general case of the finite-summation-of-integer-powers problem for arbitrary , and obtain a -th order recurrence relation that can be used to iteratively obtain the closed form polynomial for for any given . Source code is given for computing these polynomials using Maxima, an open-source (free) symbolic [...]

Finite Summation of Integer Powers (Part 1)

Assad Ebrahim — Mon, 08 Feb 2010 08:50:47 +0000

(Discrete Mathematics Techniques I)

Abstract We motivate an approach that uses recurrence relations to find closed form solutions to the finite-summation-of-integer-powers problem for any individual . The approach is illustrated for small : . Maxima, an open-source (free) software package, is used to demonstrate how a symbolic computation platform can speed up the accurate [...]