Introduction to the Theory of Analytic Functions

a₁ a₂ absolute value absolutely convergent addition theorem algebraic function amplitude angle assigned b₁ b₂ branch-point c₁ circle of convergence circuit coefficients constant continuous corresponding cosh curve defined definition denoted derivate domain elliptic function equal equation essential singular point essential singularity example expression factor finite number formula fractional fundamental region fxdx given Hence infinite infinity interval Laurent series limit-point logarithm lower limit monogenic monogenic function negative non-essential singular point one-valued analytic function one-valued function P₁ pair parallelogram path plane positive number power series prove radius of convergence rational function rational integral function real axis real numbers real variable replaced residue Riemann surface sequence sinh square root straight line stroke Suppose Taylor's theorem tends transcendental integral function uniformly convergent w₁ Weierstrass's whence x-plane x₁ zero ди