Sansone G., Gerretsen J. Lectures on the Theory of Functions of a Complex Variable. Volume 1

Groningen: P. Noordhoff, 1960. — VIII, 488 p.Classical treatise on the Theory of the Functions of a complex variable - Volume 1.Holomorphic Functions. Power Series As Holomorphic Functions. Elementary Functions
Cauchy’s Integral Theorem And Its Corollaries. Expansion In Taylor Series
Regular And Singular Points-Residues-Zeros
Weierstrass’s Factorization Of Integral Functions. Cauchy’s Expansion Of Partial Fractions. Mittag-Leffler’s Problem
Elliptic Functions
Integral Functions Of Finite Order
Dirichlet Series. The Zeta Function Of Riemann. The Laplace Integral
Summability Of Power Series Outside The Circle Of Convergence. Sum Formulas. Asymptotic Series