How to write "n choose k" as x^n y^k z^(n-k) without using Stirling

**gerritgroot** · October 4th 2012, 05:23 AM

Hi,

Is there a way to write the combinatorial (n choose k) as:

${n \choose k} =Const. \cdot x^n y^k z^{n-k}$

Without using Stirling's formula and without having a product or summation in x, y and z?

What could x=x(n,k), y=y(n,k) and z=z(n,k) be?

Thanks,

Gerrit

**chiro** · October 6th 2012, 05:03 AM

Hey gerritgroot.

You may be able to use an integral representation, but the integral itself won't have a nice analytic answer if you try and evaluate it. If you are still interested, you probably want to check out the Beta Integral:

Beta function - Wikipedia, the free encyclopedia

**gerritgroot** · October 6th 2012, 08:41 AM

Thanks, I will check that

Thread: How to write "n choose k" as x^n y^k z^(n-k) without using Stirling

LinkBack

Thread Tools

Display

How to write "n choose k" as x^n y^k z^(n-k) without using Stirling

Re: How to write "n choose k" as x^n y^k z^(n-k) without using Stirling

Re: How to write "n choose k" as x^n y^k z^(n-k) without using Stirling

Similar Math Help Forum Discussions

Ellipse: extract "minor axis" (b) when given "arc length" and "major axis" (a)

Definition clarification: "state-space", "support" and "sample space"

"How to write mathematics badly"

Why/wat is "arbitrarily" used (for) and is there a mathemical way to "write it"

"Building a patio" problem, must write an equation

Search Tags