1550251515-Classical_Complex_Analysis__Gonzalez_

766

[Set]

equivalent, 77

finite, 77

indexed collection, 77

infinite, 77

open, 95

perfect, 98

separated, 100

starlike, 85

universal, 2

Singularity:

cluster point, 661

essential, 654

isolated, 653

nonisol.ated, 653

pole of order m

removable, 499

Sink, 513

Source, 513

Spaces:

compact, 106

complete, 115

connected, 101

of continuous functions, 92-93

discrete, 121

Euclidean, 92

Frechet (see T 1 -space)

Hausdorff (see Trspace)

linear ~r vector space, 18

locally connected, 105

metric, 90-93

pseudo-Euclidean, 92

regular, 122

separable, 98

sequentially compact, 112

topological, 120

T; (i = 0, 1, 2, 3, 4), 122

Stirling's formula, 625

Stolz angle, 557

Summation of. series by using

residues, 732- 739

Symbolic method, 545-549

Index

Symmetry principle, 237

Symmetry with respect to a

circle, 236-239

Tauberian condition, 562

Tauber's theorem, 562-563

Taylor series:.

for analytic functions, 529-531

for nonanalytic fu:qctions,

522-555

Ternary semigroup,-251

Tissot's theorem, 377.:_379

Topological properties. of analytic

functions, 385:

Topologies, 121.^1

Total boundary, 416 '

Transformations, 3, 229-234

Triangle inequality, 91

. I
Uniform:
continuity, 148 ,
convergence, 197, 200-201 I

Variation, 417

bounded, 417

total, 417

Velocity:

of a fluid, 508

potential, 511

Vorticity; 513

Wallis formula, 6,24

Weierstrass doul?le series

theorem,: 540-542

M-test, 201-202

Winding number, 154..;.157

analytical represe;n~:ation,

458-460

Zeros:. ,

of analytic fu~ction~, 568-569