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| Graham R.L., Knuth D.E., Patashnik O. — Concrete mathematics |
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| Ïðåäìåòíûé óêàçàòåëü |
Planes, cutting 19
Pneumathics 164
Pochhammer, Leo 48 595
Pochhammer, symbol 48
Pocket calculators 67 330
Poincare, Jules Henri 595 605
Poisson, distribution 414 554
Poisson, Simeon Denis 457 595
Poisson, summation formula 576
Pollak, Henry Otto 588 602
Polya, George (= Gyorgy) vi 16 313 494 595 602 604 605
POLYGONS 20 360 365
Polynomial argument 158 163 210
Polynomially recursive sequence 360
Polynomials 189—191
Polynomials, degree of 158 226
Polynomials, divisibility of 225
Polynomials, reflected 325
Poonen, Bjorn 487 595 602
Porter, Thomas K. 601
Portland cement see “Concrete” (in another book)
Power series 196 (see also “Generating functions”)
Power series, formal 206 317 517
PR 367—368
Pratt, Vaughan Ronald 601
Primality testing 110 148
Prime numbers 23 105—111 442
Prime numbers, largest known 109—110
Prime numbers, Mersenne 109—110 127 507
Prime numbers, size of nth 110—111 442—443
Prime to 115
Prime-exponent representation 107 116
Princeton University ix 413
Probabilistic analysis of an algorithm 399—412
probability 195 367—424
Probability, conditional 402—405 410—411
Probability, discrete 367—424
Probability, distribution 367
Probability, generating function 380—387
Probability, space 367
Product notation 64 106
Product of consecutive odd numbers 186 256
Progression, arithmetic 26 30 362
Progression, geometric 32—33 54 114 205—206
proof 4 7
Property 23 34
Pulling out the large part 439 444
Puns ix 220
Pythagoras of Samos, theorem 495
Quadratic domain 147
Questions, levels of viii 72—73 95 497
Quicksort 28
Quotation marks xi
Quotient 81
Rabbits 296
Radix notation 11 16 109 146 148 195 233 446 511
Radix-2 representation 11—13 15 70 113
Rado, Richard 595 604
Rainville, Earl David 514 595
Ramanujan Aiyarigar, Srinivasa 316
Ramshaw, Lyle Harold 73 601 603 605
Random variables 369—372
Random variables, independent 370 413 423
Raney, George Neal 345 348 596 604
Raney, lemma 345—346
Raney, lemma, generalized 348 358
Raney, sequences 347
Rao, D. Rameswar 596 602
Rational function 207 324
Rayleigh, John William Strutt, baron 77 596
Real part 64 212 437
Reciprocity law 94
Recorde, Robert 432 596
Recurrences 1 3—4 6 10 13 78—81 103 159 323
Recurrences and sums 25—29
Recurrences, doubly exponential 97 100 101 109
Recurrences, implicit 136—138 193—194 270
Recurrences, periodic 20 179
Recurrences, solving 323—336
Recurrences, unfolding 6 100 159—160 298
Recurrences, unfolding asymptotically 442
Referee 175
Reference books 42 223 590
Reflected light rays 277
Reflected polynomial 325
Reflection law for hypergeometrics 217 235
Regions 4—5 17 19
Reich, Simeon 596 605
Relative error 438 441
Relatively prime integers 108 115—123
Remainder after division 81
Remainder in Euler’s summation formula 457 460—461 465—466
Renz, Peter Lewis viii
Repertoire method 15 19 26 44—45 63 238 298 300 358
Replicative function 100
Residue number system 126—129 144
Retrieving information 397—399
Rewards, monetary ix 242 483 510 550
Rham, Georges de 596 604
Ribenboim, Paolo 532 596 603
Rice University ix
Rice, Stephan Oswald 595
Riemann, Georg Friedrich Bernhard 205 596 602
Riemann, hypothesis 511
Riemann, zeta function 65 263—264 272 356—357 449 511 542 547 569 571 575
Rising factorial powers 48 63 211
Rising factorial powers, related to falling powers 63 298
Rising factorial powers, related to ordinary powers 249 572
Roberts, Samuel 596 602
Rocky road 36
Rodseth, Oystein Johan 596 603
Rolletschek, Heinrich Franz 499
Roots of unity 149 204 361 530 550 572
Roots of unity, modulo m 128—129
Rosser, John Barkley 111 596
Rota, Gian-Carlo 501 596
Roulette wheel 74—75
Rounding, unbiased 492
Roy, Ranjan 596 603
Rubber band 260—261 264 298 479
Ruler function 113 146 148
Running time 411—412
Ruzsa, Imre Zoltan 584
Saalschiitz, identity 214
Saalschiitz, Louis 596 603
Sample mean and variance 377—379 413
Samplesort 340
Sandwiching 157 165
Sarkozy, Andras 526 596
Sawyer, Walter Warwick 207 597
Schaffer, Alejandro Alberto 601
Schiitzenberger, Marcel Paul 605
Schinzel, Andrzej 510
Schlomilch, Oscar Xaver 597
Schoenfeld, Lowell 111 596
Schonheim, Johanen 581
Schroder, Ernst 597 604
Schrodinger, Erwin 416
Schroter, Heinrich Eduard 597 604
Scorer, Richard Segar 597 602
Searching a table 397—399
Seaver, George Thomas (= 41) 8 21 94 05 106 329
Second-order Eulerian numbers 256—257
Second-order Eulerian triangle 256
Second-order Fibonacci numbers 361
Second-order harmonic numbers 263 266 297 529
Sedgewick, Robert 601
Sedlacek, Jifi 597 604
Self reference 59 515—524 588 620
Self-certifying algorithms 104
| Self-describing sequence 66 481
Set inclusion in O-notation 432
Shallit, Jeffrey Outlaw 597 603
Sharkansky, Stefan Michael 601
Sharp, Robert Thomas 259 597
Sherry 419
Shift operator 55 188 191
Shiloach, Joseph (= Yossi) 601
Shor, Peter Williston 602
Sicherman, George Leprechaun 605
Sideways addition 12 114 146 238 529
Sierpinski, Waclaw 87 597 603
Sieve of Erastothenes 111
Sigma-notation 22—25
Signum 488
Silverman, David L. 597 604
Simple sequences and their generating functions 321
Skepticism 71
Skiena, Steven Sol 526
Slater, Lucy Joan 223 597
Sloane, Neil James Alexander 42 327 578 597 602
Small cases 2 5 9 155 306—307 316
Smith, Cedric Austen Bardell 597 602
Snowwalker, Luke 421
Solov’ev, Aleksandr Danilovitch 394 598
Solution 3 323
Sorting 28 79 175 340 434
Spanning trees 334—336 342 354—355 360
Spec 77—78 96 97 99 101
Special numbers 243—305
Spectrum 77—78 96 97 99 101 293 304
Spiral function 99
Spohn, William Gideon, Jr. 598
Sports see “Baseball Football Frisbees Golf Tennis”
Square pyramidal numbers 42
Square root of 1 (mod m) 128—129
Square root of 2 100
Square root of 3 364
Squarefree 145 151 359
Squares, sum of consecutive 41—46 51 180 233 255 270 274 353 430 456
Stack size 346—347
Stacking cards 259—260 295
Stallman, Richard Matthew 598
Standard deviation 374 376—380
Stanford University v vii ix 413 625
Stanley, Richard Peter 256 519 587 598 604 605
Staudt, Karl Georg Christian von 598 604
Steele, Guy Lewis, Jr. 598
Stegun, Irene Anne 42 578
Stein, Sherman Kopald 602
Steiner, Jacob 5 598 602
Steinhaus, Hugo Dyonizy 605
Stengel, Charles Dillon (= Casey) 42
Step functions 87
Stern — Brocot number system 119—123 146 292 504 527
Stern — Brocot tree 116—123 291—292 364 510
Stern — Brocot wreath 500
Stern, Moriz Abraham 116 598
Stewart, Bonnie Madison 586 602
Stickelberger, Ludwig 598 602
Stieltjes, constants 569 575
Stieltjes, Thomas Jan 589
Stirling convolution formulas 258
Stirling numbers 243—253 275—276 478 577
Stirling numbers as sums of products 545
Stirling numbers of the first kind 245
Stirling numbers of the second kind 244
Stirling numbers, combinatorial interpretations 244—248
Stirling numbers, convolution formulas 258 276
Stirling numbers, generalized 257—258 302 304 572
Stirling numbers, generating functions for 337
Stirling numbers, identities for 250—251 258 276 303 364
Stirling, constant 467 471—475
Stirling, formula 112 467—468 477
Stirling, formula, perturbed 440—441
STIRLING, JAMES 192 210 243 244 283 467 598
Stirling, numbers see “Stirling numbers”
Stirling, polynomials 257—258 276 297 338—339
Stirling, triangles 244 245 253
Stirling’s triangle for cycles 245
Stirling’s triangle for subsets 244
Stirling’s triangles in tandem 253
Stone, Marshall Harvey vi
Straus, Ernst Gabor 539 584 594
Subfactorial 194 238
Summand 22
Summation 21—66
Summation by parts 54—56 63 265
Summation on the upper index 160—161 176
Summation over divisors 104—105 135—137 141 356
Summation over triangular arrays 36—41
Summation, asymptotic 87—89 452—482
Summation, changing the index of 30—31 39
Summation, definite 49—50
Summation, difficulty measure for 181
Summation, factor 27—29 64 261
Summation, indefinite 48—49 55—56 161 224—230
Summation, infinite 56—62 64
Summation, interchanging the order of 34—41 105 136 183 185
Summation, parallel 159 174 208—209
Sums 21—66
Sums and differences 55
Sums and recurrences 25—29
Sums of consecutive cubes 51 63 269 275 353
Sums of consecutive integers 6 44 65
Sums of consecutive mth powers 42 269—271 274—276 352—354
Sums of consecutive squares 41—46 51 180 255 270 274 353 430 456
Sums of harmonic numbers 41 56 265—268 298—299 302 340—341
Sums of products of binomial coefficients 169
Sums, absolutely convergent 60—61 64
Sums, approximation of, by integral 45 262—263 455—461
Sums, divergent 60 517
Sums, double 34—41 105 237
Sums, doubly infinite 59 98 468—469
Sums, empty 23 48
Sums, floor/ceiling 86—94
Sums, formal 307 317—318
Sums, hypergeometric see “Hypergeometric series”
Sums, infinite 56—62 64
Sums, multiple 34—41 61
Sums, notations for 21—25
Sums, paradoxical 57
Sums, partial 48—49 55—56 161 165—166 223—230 233
Sums, tail of 452—455
Sun Tsu 126
Sunflower 277
Super generating functions 339 407
Superfactorial 149 231
Swanson, Ellen Esther viii
Sweeney, Dura Warren 598
Swinden, B.A. 602
Sylvester, James Joseph 598 602
Symmetry identities 156 254
Szegedy, Mario 510 581 599
Szego, Gabor 595 605
t-notation 22—25
Tail inequalities 414 416
Tail of a sum 452—455
Tale of a sum see “Squares”
Tangent function 273 303
Tangent numbers 273
Tanner, Jonathan William 131 599
Tanny, Stephen Michael 599 604
Tartaglia, Nicolb, triangle 155
Taylor, Brook, series 163 191 382 456—457
Telescoping 50
Tennis 418—419
Term 21
Term ratio 207—209 211—212
TeX 219 418 625
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