1550251515-Classical_Complex_Analysis__Gonzalez_

764

Metric spaces, 90-93

Minimum modulus theorem, 384,

577, 580

Mobius transformation (see

Bilinear function)

Module of periodicity, 469

Modulus:

of a complex number, 19

of a quaternion, 72

Monogenic function, 309

Morera's theorem, 495

Multiplier of the bilinear

transformation, 226

Neighborhoods, 93-95

Non-Euclidean geometry, 241-

248

Notations, 6

Open covering, 106

Operations with power series,

53'7-545

Operator, 3

Order:

of a pole, 565, 654

of a rational function, 265

of a zero, 565

Orientation of a circle, 240-241

Parallel lines, 242-243
Parseval's identity, 552
Path of integration, 414
Period:
of a function, 273, 606
of an integral, 469
Periodic functions, simply,
272-276, 605-606
Picard's theorem, 556-557, 660
Plane:
cut, 88
punctured, 88
Plemelj formulas, 494-495

Index

Poincare's

differential invariant, 246

model of Lobachevsky

geometry, 241-248

Point:

of accumulation, 97

of contact, 97

isolated, 97

Point arc, 151

Poisson's

formulas, 504-506

summation formula, 613

Pole, 264, 654

Power series, 203-210

operations with, 537-545

radius of convergence, 205-

208, 529

reversion, 543-544, 752-754

Power set, 3

Primitives of an analytic

function, 467-469

Principal:

branch of inverse circular

functions, 301, 304-305

branch of inverse hyperbolic

functions, 301-302, 305

directions, 373, 377, 379

logarithm, 55, 297

nth root, 47

part of .6.u, 313

part of a function at an

isolated essential

singularity, 654

part of a meromorphic

function at a pole, 654

region, 88

value of arg z, 29

value of zo:, 56, 299

Ptolemy's theorem, 250

Quaternions, 71-72

1835 26

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