Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

I want to compute $\int_0^z t^{-b}e^t \,dt$ where $b>0$ by using incomplete gamma function. Can I rewrite my integral as a form of the incomplete gamma function?

share|cite|improve this question

Making the change of variables $t=-u$, we have $$ \int_0^z t^{-b}e^t \,dt = -\int_{0}^{-z} (-u)^{-b}e^{-u} \,du=(-1)^{-b+1}\int_{0}^{-z} t^{-b}e^{-u} \,du=(-1)^{1-b}\gamma(1-b,-z), $$

where $\gamma(s,x)$ is the lower incomplete gamma function.

share|cite|improve this answer

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.