complex-analysis
The Gamma function
The factorial extended off the positive integers by an improper integral, then continued by its own functional equation to a meromorphic function on the whole plane with simple poles at the non-positive integers.
Taught in
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The Gamma function
Complex Analysis
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The functional equation and the reflection formula
Complex Analysis
Requires
- analytic-continuation required
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liouvilles-theorem
helpful
The reasoning that pins down an entire function from growth/boundedness estimates on ever-larger contours is the same style of argument used to justify the Gamma function's continuation and its functional equation.
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gamma-and-beta-functions
helpful
The real-variable Gamma function from vector-analysis, defined by the same improper integral, before this course continues it off the positive real axis.
Required by
Nothing in the catalog needs this yet.
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