incomplete gamma function recurrence formula

The incomplete gamma functionDlmfDlmfDlmfDlmfMathworldPlanetmath satisfies the following recurrence formula:


This can be derived by integration by parts:

0xe-tta𝑑t = -0xta𝑑e-t
= a0xta-1𝑑e-t-xae-x

In terms of other variants of the incomplete gamma function, the recursion relation appears as follows:

P(a+1,x) = P(a,x)-xae-xΓ(a+1)
γ*(a-1,x) = xγ*(a,x)+e-xΓ(a)
Title incomplete gamma function recurrence formula
Canonical name IncompleteGammaFunctionRecurrenceFormula
Date of creation 2013-03-22 15:36:50
Last modified on 2013-03-22 15:36:50
Owner rspuzio (6075)
Last modified by rspuzio (6075)
Numerical id 6
Author rspuzio (6075)
Entry type Theorem
Classification msc 30D30
Classification msc 33B15