1550251515-Classical_Complex_Analysis__Gonzalez_

Index

Improper real integrals, 684-687

evaluation by residues,

687-732

Incomplete gamma function, 646

Index (see Winding number)

Infinitely large, 141

Infinitesimals, 139-140

Infinity, 58-59

Integrals, 409-419, 486-490

Integrand, 414

Integration by parts, 433

Interior:

of a curve, 158

of a set, 96

Inverse:

function, 5, 356-358, 751-757

image, 5

mapping, 5

Inversion of a series (see Power

series, reversion)

Jensen circles, 572
Jensen-Walsh theorem, 572-573
Jordan arc, 156
curve, 157-158
Jordan's inequality, 680
lemma, 680-681
Joukowski's functions, 268

Karman-Trefftz profiles, 269
Kasner circle, 349-350
for the inverse function, 362
K-quasiconformal mapping, 393
Kummer's test, 193-194

Lagrange's identity, 23
Laguerre polynomial, 494
Laplace differential operator, 321
equation, 321, 332-333
formula, 498
transform, 619, 719-721
Laplacian, 321

Lattice, 448

function, 401

763

Laurent series expansion, 594-

599

Laws, 8, 79-80

Lebesgue's covering lemma, 115

number, 115

Legendre polynomial, 493

Limit of a function, 132-139

of a sequence, 174, 197

Limit point, 87

Limit superior (inferior) of a real

sequence, 180-1'82

Line integral:

complex, 414

real, 433-434

Lines, 81-85, 89-90

Locally bounded function, 464

Logarithmic function, 296-298

Lucas theorem, 571

Magnification ratio, 343, 345,

366-371

Mancill's formula, 437

Mapping, 3-6

bijective, 5

conformal, 365

directly, 365

indirectly, 365

isogonal

directly, 364

indirectly, 365

interior, 149

isometric, 119

nonconformal, 366-379

one-to-one (injective), 5

onto (surjective ), 4

Maximum modulus theorem,

383, 575-576, 580

Mellin transform, 707

Meromorphic functions, 664

zeros and poles, 7 40-7 4 7