Concept explainers
We have encountered the gamma function Γ(α) in our study of Bessel functions in Section 6.4 (page 263). One definition of this function is given by the improper integral
Use this definition to show that Γ(α + 1) = αΓ(α). When α = n is a positive integer the last property can be used to show that Γ(n + 1) = n!. See Appendix A.
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