From 61b48fd8baae321daf294ebf670ef4906240d260 Mon Sep 17 00:00:00 2001 From: Holden Rohrer Date: Wed, 5 May 2021 19:03:09 -0400 Subject: homeworks and attendance quizzes for kang --- kang/att4 | 19 +++++++++++++++++++ 1 file changed, 19 insertions(+) create mode 100644 kang/att4 (limited to 'kang/att4') diff --git a/kang/att4 b/kang/att4 new file mode 100644 index 0000000..8c19a35 --- /dev/null +++ b/kang/att4 @@ -0,0 +1,19 @@ +Q1) Find power series + +f(z) = e^{-z}/z^2 for 0<|z|<\infty + +e^{-z} = 1 - z + z^2/2! - z^3/3! + z^4/4! ... +f(z) = 1/z^2 - 1/z + 1/2! - z/3! + z^2/4! ... + +Q2) + +f(z) = {1+2z^2 \over z^3 + z^5} |z|<1 + = {1 \over z^3(1+z^2)} + {2\over z(1+z^2)} + +{1\over (1+z^2)} = 1 - z^2 + z^4 - z^6 ... + +{1\over z^3(1+z^2)} = 1/z^3 - 1/z + z - z^3 ... +{2\over z(1+z^2)} = 2/z - 2z + 2z^3 - 2z^5 ... + +f(z) = +1/z^3 + 2/z - 1/z - 2z + z + 2z^3 - z^3 - 2z^5 ... -- cgit