Generating Functions, Taylor Series, Taylor Theorem, Central Limit Theorem, Deep Dives.
k = 2. The second part is the remainder of the infinite series: Taylor series expansion of M_Z(t/√n) at a = 0 split into two parts (Image by Author) In the above series, M⁰, M¹, M², etc. are the 0-th, 1st, 2nd, and so on derivatives of the Moment Generating Function M_Z(t/√n) evaluated at (t/√n) =