Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Gamma Function Integral

  1. May 22, 2013 #1
    This is mostly calculus, but the question is computer based, I think.

    The antiderivative of the gamma function is, fairly trivially, ##\displaystyle \int_{0}^{+\infty}\frac{t^{z-1}}{e^{t}\ln{t}}-C##, where C is an arbitrary constant.

    Why does Wolfram Alpha have trouble calculating the convergence of that integral at any given point?
     
  2. jcsd
  3. May 22, 2013 #2

    mathman

    User Avatar
    Science Advisor
    Gold Member

    Definite integrals do not have a constant of integration. What values of z are you having trouble with? The integrand blows up at t = 0 for Re(z) <1 and the integral diverges for z = 0, -1, -2, etc.
     
  4. May 22, 2013 #3
    That's not what I'm saying. :tongue:

    I'm saying that ##\displaystyle \int \Gamma(z) dz = \int\int_{0}^{+\infty}\frac{t^{z-1}}{e^{t}}\, dt \ dz = \int_{0}^{+\infty}\frac{t^{z-1}}{e^{t}\ln{t}}-C##. I'm evaluating the antiderivative, or "indefinite" integral, of the Gamma function. It's fairly evident that I used Fubini's theorem, because it's the only sensible way to obtain that result.

    I'm asking why the antiderivative of the Gamma function can't be evaluated by Wolfram Alpha.
     
  5. May 23, 2013 #4

    mathman

    User Avatar
    Science Advisor
    Gold Member

    I now understand what you did. However I have never worked with Wolfram Alpha, so I can't help you there.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook