some formulas involving rising factorial

Recall that, for a and n a nonnegative integer, the rising factorialDlmfMathworldPlanetmath (a)n is defined by


The following results hold regarding the rising factorial:

  • For all a, we have (a)0=1.

  • For all nonnegative integers n, we have (1)n=n!.

  • The binomial coefficientsDlmfDlmfMathworldPlanetmath are given by

  • The rising factorial relates to the gamma functionDlmfDlmfMathworldPlanetmath. One relation is given by the formula


    This formula can be used to extend the definition of rising factorial so that n can be any complex number provided that a+n is not a nonpositive integer.

  • Another relation between the rising factorial and the gamma function is given by

Title some formulas involving rising factorial
Canonical name SomeFormulasInvolvingRisingFactorial
Date of creation 2013-03-22 17:49:12
Last modified on 2013-03-22 17:49:12
Owner Wkbj79 (1863)
Last modified by Wkbj79 (1863)
Numerical id 4
Author Wkbj79 (1863)
Entry type Result
Classification msc 05A10