- #1
TylerH
- 729
- 0
I mean an extension analogous to the extension of factorial to gamma(ignoring the shift).
I want to extend the iterative number, usually written below the sigma, to be a real number, rather than an exclusively natural number.
The easiest way I can think of is to convert the sum into a definite integral, since the bounds of an integral can be any real number(or infinity). Is there any known way to convert sigma sums into definite integrals? It seems as if it should be possible, seeing as the integral is just an infinite sum of infinitesimals.
I want to extend the iterative number, usually written below the sigma, to be a real number, rather than an exclusively natural number.
The easiest way I can think of is to convert the sum into a definite integral, since the bounds of an integral can be any real number(or infinity). Is there any known way to convert sigma sums into definite integrals? It seems as if it should be possible, seeing as the integral is just an infinite sum of infinitesimals.