760
Borel-Caratheodory theorem,
586-587
~
Branch, 5, 2~6 ." . .---·
algebraic, 287:2~6::.:.::c::::--.. I
(^1) ogant.. 'h rmc,~. \^298 .. '·. ., ' >,''<·.r-~ -<......._., ,, .. :---. ..
7''\ ·" 11 ~··· \• \' \
Bromwich int\gr, .. ·~J;,~7· t~.! · .. > ... ·. l... ""'·
~\ \ ".'\ >. J }
Calculus of sets,.l7:~".'i8 ')<). · ;~: "\ ..•..• tx~Y
Cantor's lemma, ~3~~.14;\ ''~.·~
theorem, 118 '•. "·, \ "'
Cartesian product, ~· 1\.
Cauchy-Goursat theore~,,,,, ~··.
441-452 ·~ "·,~\. '.
generalizations, 453-457 ~'< .~.~:·. \
464-465 ""·· \'v'~ "~~
Cauchy-Hadamard formula, 204 · '•.~\
Cauchy-Liouville theorem, 496 t
for nonanalytic functions, 497
Cauchy-Riemann equations,
317-318, 335
complex form, 327
generalized, 392, 394-398, 400
in polar coordinates, 332
Cauchy's
condition, 115, 182-183,
186-187
formulas for the derivatives,
490-491
fundamental theorem, 435-
437
inequality, 495-496
integral formula, 4 73-4 75
generalizations, 4 76-483
principal value, L180, 684-685
residue theorem, 675-678
root test, 193
rule for product of two series,
191-192
Cauchy-Taylor expansion,
529-531
Chain, 160
IndexChange of parameter, 153-154,
410, 426
Characteristic coefficients, 396
lines, 381
Circle, 87-90
Circle of convergence, 205
Circular ar.c,. 88
~~ "
f.o/1ctions\27~.22883. , 300-305
Circulation, 510_:\__
Co~omJih,l J ~.
Compactness, 106'-115 "-<).;'-
c omp 1. emenj;ation,. 79 "' ~.f/)"' ··h5l! -
Completeness, 115-120 , V ·
Complex:
conjugate, 12-14
function, 125-126
integration, 409, 413-420
number, 7-12
algebraic, 285
axiomatic foundation, 73
binomial form, 12
exponential form, 32
general binary, 66-68
geometric representation,
27-29, 35-39
as a linear system, 17-18
logarithm, 54-56
ordering, 15-17
polar form, 30-32
powers, 42-44, 51-54,
56-58
transcendental, 285
Components:
of a complex function, 126
of a complex number, 7
of a set, 102
Confluent hypergeometric
function, 641-645
Conformal mappings, 363-366
Connectivity of a region, 169
Connectness, 100-106