📄 invindex.tex
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327--330: change327--330: coins327: P\'olya330: Andrews330: R\=am\=anujan Aiya\.ng\=ar, Sr\=\i niv\=asa330: partitions\sub of a number331: Fibonacci numbers\sub closed forms for331: bracket notation\sub for coefficients331: coefficient extraction331: convergence\sub of power series331: formal power series331: philosophy331: power series\sub formal332: Bell, Eric Temple332: Henrici, Peter Karl Eugen332: Niven, Ivan Morton333--334: generating functions\sub for convolutions333: convolution333: derivative operator\sub with generating functions333: disease333: integration\sub of generating functions334: generating functions\sub table of manipulations335: generating functions\sub for simple sequences337--340: Fibonacci numbers\sub ordinary generating functions for337--340: generating functions\sub for Fibonacci numbers337--350: recurrences\sub solving337: solution338--341: partial fraction expansions338--346: rational generating functions338: rational functions339: polynomials\sub reflected339: reflected polynomials340--341: rational generating functions\sub expansion theorems for340: L'Hospital, Guillaume Fran\c{c}ois Antoine de, marquis de Sainte Mesme, rule341: Sloane343: Mathews343: Seaver344--346: change\sub large amounts of344: calculators\sub failure of344: nearest integer\sub rounding to344: pocket calculators\sub failure of344: rounding to nearest integer345--346: graphs of functions\sub partial sums of a sequence346--348: divergent sums\sub considered useful346--348: factorial function346: closed form\sub pretty good347: $\vartheta$347: theta operator348--350: counting\sub spanning trees348--350: spanning trees\sub of fans348--350: trees\sub spanning348: fans348: formal power series348: power series\sub formal349: empty case\sub for spanning trees349: null case\sub for spanning trees351--352: Stirling numbers\sub generating functions for351--352: generating functions\sub for Stirling numbers351--352: generating functions\sub for harmonic numbers351--352: harmonic numbers\sub generating function for351--353: generating functions\sub for special numbers351: Bernoulli numbers\sub generating function for351: Eulerian numbers\sub generating function for351: Fibonacci numbers\sub ordinary generating functions for351: generating functions\sub for Bernoulli numbers351: generating functions\sub for Eulerian numbers351: generating functions\sub for Fibonacci numbers351: generating functions\sub of generating functions352: Stirling\sub polynomials352: polynomials\sub Stirling353--364: convolution353--364: generating functions\sub for convolutions353: generating functions\sub for Eulerian numbers353: generating functions\sub of generating functions353: generating functions\sub super353: super generating functions354--355: harmonic numbers\sub sums of354--355: sums\sub of harmonic numbers354: samplesort354: sorting\sub samplesort356: counting\sub spanning trees356: spanning trees\sub of fans356: trees\sub spanning357--359: counting\sub parenthesized formulas357--359: parentheses357: clich\'es358--360: Catalan numbers\sub combinatorial interpretations359--360: Raney\sub lemma359--362: partial sums\sub required to be positive359: Raney, George Neal359: mountain ranges360--361: Raney\sub sequences360--361: stack size361: Catalan361: Catalan numbers\sub generalized361: Fuss, Nicola{\u\i} Ivanovich361: Fuss\sub Fuss--Catalan numbers361: Jeopardy362: Raney362: Raney\sub lemma, generalized363: Lambert363: binomial series363: generalized binomial series364--365: derivative operator\sub with generating functions364--369: exponential generating functions364--369: generating functions\sub exponential364: egf: exponential generating function364: exponential series364: generalized exponential series365: Bernoulli numbers\sub generating function for365: binomial convolution365: convolution\sub binomial365: generating functions\sub for Bernoulli numbers365: integration\sub of generating functions366--368: sums\sub of consecutive $m$th powers367--368: Bernoulli\sub polynomials367--368: polynomials\sub Bernoulli367: binomial convolution367: convolution\sub binomial367: cubes367: probability distributions367: squares367: sums\sub of consecutive cubes367: sums\sub of consecutive squares368--369: counting\sub spanning trees368--369: spanning trees\sub of complete graphs368--369: trees\sub spanning368: complete graph369: exponential series369: generalized exponential series369: generating functions\sub for convolutions370--371: Dirichlet\sub generating functions370--371: M\"obius\sub function370--371: Riemann's zeta function\sub dgf's involving370--371: generating functions\sub Dirichlet370--371: zeta function\sub dgf's involving370: Dirichlet, Peter Gustav Lejeune370: dgf: Dirichlet generating function370: generalized harmonic numbers370: harmonic numbers\sub generalized370: kernel functions370: summation\sub over divisors371: Riemann's zeta function\sub as infinite product371: domino tilings371: multiplicative functions371: phi function\sub dgf for371: totient function\sub dgf for371: zeta function\sub as infinite product372: Kent, Clark (= Kal-El)372: Raney\sub lemma372: repertoire method\sub for Fibonacci-like recurrences373: Bell\sub numbers373: Dirichlet\sub generating functions373: Riemann's zeta function\sub dgf's involving373: convolution\sub identities for373: convolution\sub polynomials373: generating functions\sub Dirichlet373: partitions\sub of a set373: polynomials\sub convolution373: squarefree373: zeta function\sub dgf's involving374: bricks374: change374: counting\sub spanning trees374: differentiably finite power series374: partial fraction expansions\sub not always easiest374: polygons\sub triangulation of374: polynomially recursive sequence374: spanning trees\sub of wheels374: stacking bricks374: trees\sub spanning374: triangulation374: wheel375: Fibonacci numbers\sub second-order375: complex numbers\sub roots of unity375: domino tilings\sub ordered pairs of375: roots of unity375: second-order Fibonacci numbers376: arithmetic progression376: exact cover376: partial fraction expansions\sub for easy summation and differentiation376: partial fraction expansions\sub powers of377: DNA, Martian377: Martian DNA377: binary partitions377: generating functions\sub for minima377: minimum377: partitions\sub of a number377: permutations\sub up-down377: up-down permutations378: $\sqrt3$ ($\approx1.73205$)378: Eulerian numbers378: Newtonian generating function378: Stirling numbers\sub identities for378: generating functions\sub Newtonian378: sorting\sub possible outcomes378: square root\sub of $3$378~(exercise~44): preferential arrangements379: Kissinger, Henry Alfred379: domino tilings379: polygons\sub dissection of379: trigonometric functions\sub related to tilings380: differentiably finite power series380: pentagonal numbers380: triangular numbers381--382: Pr381--382: elementary events381--384: dice381--438: discrete probability381--438: probability381--438: probability\sub discrete381--438: theory of probability381: Feller, William381: discrete probability\sub defined381: probability\sub spaces382: dice\sub fair382: dice\sub loaded382: event382: fair dice383--386: random variables384--399: mean (average) of a probability distribution384: average384: independent random variables384: joint distribution384: median384: mode384: probability distributions\sub joint385--386: $E$: expected value385--387: expected value385: median385: mode386: independent random variables\sub products of386: independent random variables\sub sums of387--388: greed387--388: lottery387--398: $V$: variance387--398: variance of a probability distribution388: $\sigma$: standard deviation388: cheating388: standard deviation390--391: Chebyshev\sub inequality390--394: standard deviation391--393: empirical estimates391--393: sample mean and variance391: Law of Large Numbers391: insurance agents392: dice\sub supposedly fair392: unbiased estimate393--394: fixed points393--394: football victory problem\sub mean and variance393--394: permutations\sub fixed points in393--394: permutations\sub random394--401: generating functions\sub for probabilities394--401: probability\sub generating functions394: pgf: probability generating function395--396: probability distributions\sub uniform395--396: uniform distribution395: expected value\sub using a pgf396--398: independent random variables\sub sums of396: L'Hospital396: Taylor397--401: cumulants397: Thiele, Thorvald Nicolai398--399: moments398: Thiele399--400: dice\sub pgf for399: random constant400--401: fixed points\sub pgf for400--401: football victory problem\sub mean and variance400--401: permutations\sub fixed points in400--401: permutations\sub random401--402: binomial distribution401--402: probability distributions\sub binomial401--410: coins\sub flipping401--410: flipping coins401: Lincoln, Abraham401: biased coin401: cheating401: coins\sub biased401: coins\sub fair401: coins\sub spinning401: fair coins401: spinning coins402--403: binomial distribution\sub negative402--403: negative binomial distribution402--403: probability distributions\sub negative binomial402: Bernoulli\sub trials405: Doyle405: Markov, Andre{\u\i} Andreevich (the elder), processes405: Watson405: automaton405: finite state language408--410: Alice408--410: Bill408--410: Penney ante408--410: paradoxes\sub coin flipping408: Penney, Walter Francis408: Solov'ev, Aleksandr Danilovitch410: Conway, John Horton410: nontransitive paradox410: odds410: transitive law\sub failure of411--413: information retrieval411--413: retrieving information411--413: searching a table411--426: hashing411: Knuth413--426: algorithms413--426: analysis of algorithms413--426: probabilistic analysis of an algorithm413: running time415: binomial distribution415: probability distributions\sub binomial416--419: conditional probability416--419: probability\sub conditional416: pi ($\approx3.14159$\sub as canonical constant417--418: clearly, clarified417--418: trivial417: dice\sub fair417: fair dice417: obvious, clarified418--419: uniform distribution418: Erd\H os, P\'al (= Paul)418: permutations\sub fixed points in419--425: $V$: variance419--425: variance of a probability distribution419: Zipf, George Kingsley, law420--421: probability distributions\sub uniform421--422: exponential generating functions421--422: generating functions\sub exponential421: generating functions\sub for convolutions421: generating functions\sub of generating functions421: generating functions\sub super421: super generating functions423--425: average\sub variance423: pi ($\approx3.14159$\sub as canonical constant423: pizza424--425: conditional probability424--425: probability\sub conditional425--426: running time426: asymptotics\sub of hashing427: Princeton University427: Stanford University427: dice\sub probability of doubles427: empirical estimates427: independent random variables427: sample mean and variance428--429: $\sim$: is asymptotic to428--429: Poisson\sub distribution428--429: cumulants\sub of Poisson distribution428--429: probability distributions\sub Poisson428: Chebyshev\sub inequality428: binomial distribution428: binomial distribution\sub negative428: composition of generating functions428: fixed points\sub pgf for428: football victory problem428: generating functions\sub composition of428: mixture of probability distributions428: negative binomial distribution428: permutations\sub random428: probability distributions\sub binomial428: probability distributions\sub composition or mixture of428: probability distributions\sub negative binomial428: tail inequalities428: variance of a probability distribution\sub infinite429: cumulants\sub third and fourth429: dice\sub fair429: dice\sub loaded429: football victory problem\sub generalized429: sample third cumulant429: unbiased estimate430--432: coins\sub flipping430--432: flipping coins430: Alice430: Bill430: Chebyshev\sub inequality430: Penney ante430: Schr\"odinger, Erwin430: coins\sub fair430: fair coins430: hashing430: pentagon430: tail inequalities430: worm\sub and apple431: dice\sub loaded431: dice\sub nonstandard431: golf432--433: knockout tournament432--433: tennis432--433: tournament432: Dirichlet\sub generating functions432: Dirichlet\sub probability generating functions432: \TeX432: average\sub of a reciprocal432: binomial distribution432: cumulants\sub of binomial distribution432: generating functions\sub Dirichlet432: probability distributions\sub binomial433: Banach, Stefan433: sherry433: wine434--435: frisbees434: diphages434: pentagon434: phages434: triphages434: war435: Snowwalker, Luke435: Wham-O435: trigonometric functions\sub related to probabilities436--437: doubloons436--437: lottery437--438: coins\sub flipping437--438: flipping coins437: Penney ante437: cards\sub shuffling437: frisbees437: independent random variables\sub pairwise437: median437: mode437: trigonometric fu⌨️ 快捷键说明
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