Assignment #8

Due: 24 February, 1998

  1. Define Gamma(x) by
    Gamma(x) = integral_0^infinity t^{x-1}e^{-t} dt .

    a. Verify that this definition makes sense whenever x > 0. [3]

    b. Show that Gamma(x)(1) = 1 and that Gamma(x+1) = xGamma(x) whenever x > 0. [3]

    c. If n is a positive integer, what is Gamma(n)? [1]

  2. Determine which continuous functions f(x) satisfy

    f^2(x) = integral_0^x f(t) dt . [3]

Solution to Assignment #8
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