count the number of , 328
order k, 277, 280, 288, 294
residue, 294
simple, 278 , 294
Polynomial
factorization, 246
Legendre, 240
roots, 32, 246
zeros,32, 246
Positive orientation, 40, 215
Potential, 44 6
complex, 446, 468 , 500
curve, 119
electrostatic, 446, 459 , 500
velocity, 446, 468
Power series, 147
Cauchy product, 262
convergence. 148
differentiation, 150
division, 286
multiplication, 262
radius of convergence, 148
uniqueness, 261
Powers, 171
complex number, 3 1, 171, 173
De Moivre's formula for, 32
rationa l, 173
Primitive nth root, 34
Principal branch
z^112 , 64, 80
z^1 /~, 68
zC, 171
logz, 163
Principal value
argz, 2,3
logz, 163
zlfn. 68
Principle maximum harmonic
functions, 24S
Principle maximum modulus
analytic functions, 242, 244
Principle of the argument, 328
Product Cauchy, 130
Product series, 262
Punctured disk, 41
Quadratic Formula, 36
Quotient complex numbers, 9
Quotient •eries, 286
Radius of convergence, 148
Range of function, 49
Ratio test, 143, 148
Rational function, 328
Rational function integral, 306,
308
Re(z), 13, 51
Real axis, 16
IND.EX 631Reciprocal transformation, 85
Recursion formula difference
equation, 360, 373, 379
Region, 44
Region of convergence
z..transform, 338
Removable singularity, 277
Repararneterization, 209
Residue, 291, 294
application, 308, 312, 317, 323
calculation, 294
difference equation, 362, 349
poles, 294, 343
singular points, 291
theorem, 293
Response
amplitude, 374, 381
mechanical system, 532
output , 380
Riemann
Riemann, Bernhard, 100
mapping theorem, 423
sphere, 86
s um, 201
surface (z2 - 1)^112 , 416
surface log z, 168
surface z^112 , 82
theorem of, 287
Risch-Norman algorithm, 304
RLC circuit, 185
Root
complex number, 33
test for series, 145, 148
unity, 33
Rotation trans formation> 56
Rouche's t heorem, 333
Rule L'Hopital's, 286
Scale factor, 400
Schwarz-Christoffel
formula, 487
t heorem, 48 7
t ransformation> 487
Sequence, 123
Cauchy, 127
causal, 373
convergence, 124
divergence, 124
limit, 124
Series
binomial, 264
comparison test, 130
convergence, 12 8, 14 5, 148, 257
differentiation, 150
divergence, 128
Fourier, 275, 513
geometric, 141