Is there a way to specify integer arguments while integrating in Mathematica

Question

I am trying to evaluate the following integral in Mathematica:

Integrate[u ^(m + 1)*Exp[-(u^2)/(2*rho)]*(u^2 - eps)^(j + k/2 - 1) , {u, Sqrt[eps],Infinity}]

I want to specify that for me, m and j are nonnegative integers, and k is a positive integer. Is there a way to do that in Mathematica? Thanks in advance!.

Thanks to @Bill's answer below, I was able to use:

Integrate[
 u ^(2*m + 1)*Exp[-(u^2)/(2*rho)]*(u^2 - eps)^(j + k/2 - 1) , {u, 
  Sqrt[eps], Infinity}, 
 Assumptions -> 
  m >= 0 && j >= 0 && k > 0 && Element[m | j | k, Integers] ]

However, the answer I get: involves Gamma(-m) when I use 2*m as an even integer (m here is an integer) which does not exist.

Bill · Accepted Answer · 2024-08-28 13:50:50Z

1

Try

Integrate[..integrand.. , ..domain..,
  Assumptions->m>=0&&j>=0&&k>0&&Element[m|j|k,Integers]]

answered Aug 28, 2024 at 13:50

Bill

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2 Comments

user3236841 Over a year ago

Thank you! This helps, however, I still get an answer involving Gamma[-m/2] which I for even integers m does not exist.

user3236841 Over a year ago

I will however mark your answer as correct because it does answer the specific question asked here.

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