Generating Functions, Taylor Series, Taylor Theorem, Central Limit Theorem, Deep Dives.
expansion, and a residue term that captures the summation: Taylor series expansion of M_Z(t/√n) at a = 0 expressed as an order-2 Taylor polynomial and a remainder term (Image by Author) We’ve already evaluated the order-2 Taylor polynomial. So our task of finding the MGF of Z is now further reduced