1550251515-Classical_Complex_Analysis__Gonzalez_

762

Factorial function, 630-632
Finite increments formula, 355
Finite intersection property, 109
Fixed points, 225
Fluid:
irrotational, 510
solenoidal, 510
Fluid dynamics, 508-517
Function( s ):
analytic, 309
generalized, 390-401
associated with a given
function, 130-131
bicontinuous, 149
of classes C(A), 'D(A), 1i(A),
320
continuous, 142-149
along an arc, 157
uniformly, 148
defined by
real improper integrals,
526-529
sequences, 522-523
series, 521-522
discontinuous, 144
geometric representation,
127-130
harmonic, 321
holomo:rphic (see Analytic)
light, 385
meromorphic, 664
monogenic, 309
multiple-valued, 7, 485-501
open, 149
polygenic, 342
polynomial, 260-264
primitive, 409
rational, 264-267
reciprocal, 131, 218-219
regular at a point, 650
single-valued, 7
singulru: at a point, 653

[Function( s)]

subharmonic, 328

Functional, 662

Index

Functional equation of the

gamma function, 617

Gamma function, 613-627

graphs, 626

Gauss test, 196

formula (see Euler formula)

Graph of f:X -t Y, ·5

Green's theorem, 436

complex form, 441

discrete form, 448

Hadamard's three-circles

theorem, 589-590

Half-planes, 85-86

Harmonic conjugate, 322

>.-harmonic conjugate, 396

Harmonic function, 321

>.-harmonic, 396

Heaviside function, 485

Homeomorphism, 149

Homology, 167, 461

Homotopy, 161

of arcs with fixed endpoints,

162

of curves, 162, 462

linear, 163

Hurwitz polynomial, 272

theorem, 747-748

Hyperbolic functions, 275-276,

301-302, 305

Hypercomplex numbers, 69-72

Hypergeometric function, 635-

641

Identity principle:

for analytic functions, 569-570

for polynomials, 261

for power series, 209-210