Proposition: Gamma Function
The improper integral $\int_0^\infty \exp(-t)t^{x-1}dt$ is convergent if and only if $x > 0.$ For a given $x>0$, we call this limit the Gamma function $\Gamma(x)$ and set $$\Gamma(x):=\int_0^\infty \exp(-t)t^{x-1}dt,$$ where $\exp$ denotes the real exponential function.
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Table of Contents
Proofs: 1
- Proposition: Gamma Function Interpolates the Factorial
Mentioned in:
Proofs: 1
Propositions: 2
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References
Bibliography
- Forster Otto: "Analysis 1, Differential- und Integralrechnung einer Veränderlichen", Vieweg Studium, 1983
- Heuser Harro: "Lehrbuch der Analysis, Teil 1", B.G. Teubner Stuttgart, 1994, 11th Edition
