ABSTRACT
Differentiations) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 633 10.7 Uniform Convergence of Power Series . . . . . . . . . . . . . . . . . . . . . . . . . . 636 10.8 Formulas of Parseval, Schwarz, and Poisson . . . . . . . . . . . . . . . . . . . . 648 10.9 Functions Defined by Integrals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 656
Let 〈sn(z)〉 be a sequence of one-valued functions, where each function is defined in a bounded closed domain D. The sequence 〈sn(z)〉 of functions is said to be convergent at a point z0 ∈ D if the sequence of complex numbers 〈sn(z)〉 tends to a definite finite limit. If the sequence 〈sn(z)〉 converges at each point of D, it is said to be point-wise convergent in D and the limit function s(z) of the sequence 〈sn(z)〉 is defined at each point of D by the equation
s(z) = lim n→∞ sn(z).
