MATH 141 Chapter Notes -Gamma Function, Positive Real Numbers, Multiplication Theorem
Document Summary
In this topic we will look at the gamma function. This is an important and fascinating function that generalizes factorials from integers to all complex numbers. We look at a few of its many interesting properties. In particular, we will look at its connection to the laplace transform. We will start by discussing the notion of analytic continuation. We will see that we have, in fact, been using this already without any comment. This was a little sloppy mathematically speaking and we will make it more precise here. If we have an function which is analytic on a region , we can sometimes extend the function to be analytic on a bigger region. 0 e3e (1) (though we switched the variable from. We recognize this as the laplace transform of () = e3 to ). The integral converges absolutely and is analytic in the region = {re() > 3}. That is, can we nd a region a function.
