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MathGroup Archive 1999

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Re: Integer Assumptions in Integrations

  • To: mathgroup at smc.vnet.net
  • Subject: [mg20179] Re: [mg20153] Integer Assumptions in Integrations
  • From: BobHanlon at aol.com
  • Date: Sun, 3 Oct 1999 21:07:43 -0400
  • Sender: owner-wri-mathgroup at wolfram.com

Will,

Integrate[t^(a - 1)*Exp[-t], {t, q, Infinity}]

Gamma[a, q]

This answer is not simpler for integers. I think you want FunctionExpand

Table[Gamma[a, q], {a, 5}] // FunctionExpand // Simplify

{E^(-q), (q + 1)/E^q, (q^2 + 2*q + 2)/E^q, 
  (q^3 + 3*q^2 + 6*q + 6)/E^q, 
  (q^4 + 4*q^3 + 12*q^2 + 24*q + 24)/E^q}


Bob Hanlon

In a message dated 10/2/1999 8:11:29 AM, wcooper1 at san.rr.com writes:

>How can I set a variable assumption to be an integer in an integration
>
>calculation?
>
>e.g. The incomplete gamma function is defined as Gamma[a,q] =
>Integrate[t^(a-1)*Exp[-t], {t, q, Infinity}]
>
>I want to set the assumption that 'a' is always an Integer.
>
>I don't want to round 'a' to the next lowest integer, i.e. 
>Integrate[t^(Integer[a]-1)*Exp[-t], {t, q, Infinity}]
>
>I just want to indicate that 'a' only assumes integer values.
>


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