A.1 Some useful Taylor series
We collect here some useful Taylor series used throughout the text, z denotes a complex variable, and the expression on the right denotes the convergence region.
A.2 “” notation
Definition A.1 Let F(x) be a real function. We say that “F(x) is of order f(x) as x tends to a” and write F(x) = f(x)) as x → a, if and only if there exist two constants C > 0 and δ > 0 such that |F(x)| ≤ C |f(x)| when |x − a| < δ.
For example, if F(x) is n + 1 times differentiable around x = a, then by Taylor’s theorem,
where the remainder term satisfies Rn(x) = ((x − a)n+1). Here, and many times when it is clear by context, we omit “as ...