invindex.tex

Concrete_Mathematics_2nd_Ed_TeX_Source_Code

146: divides exactly
146: divides exactly\sub in factorials
146: exactly divides
146: exactly divides\sub in factorials
146: nu function: sum of digits\sub other radices
146: pi ($\approx3.14159$\sub Stern--Brocot representation of
146: ruler function
146: sideways addition
147: Euclid (= xxx)
147: Euclid\sub numbers
147: Euler\sub pronunciation of name
147: Euler\sub theorem
147: algebraic integers
147: divisibility\sub by~$3$
147: inverse modulo $m$
147: prime algebraic integers
147: quadratic domain
147: unique factorization
147: unit
148: Fermat's theorem (= Fermat's Little Theorem)\sub converse of
148: Ketcham, Henry King
148: LeChiffre, Mark Well
148: Stern--Brocot tree
148: Wilson
148: Wilson, Martha
148: baseball
148: primality testing
148: ruler function
149: Fermat's theorem (= Fermat's Little Theorem)
149: M\"obius\sub function
149: complex numbers\sub roots of unity
149: cyclotomic polynomials
149: multinomial theorem
149: polynomials\sub cyclotomic
149: roots of unity
149: superfactorials
150--151: gaps between primes
150--151: prime numbers\sub gaps between
150: $e$ ($\approx2.71828$)\sub representations of
150: Egyptian mathematics
150: Euclid\sub numbers
150: Farey\sub consecutive elements of
150: Fermat's Last Theorem
150: Stern--Brocot number system\sub representation of $e$
150: fractions\sub unit
150: totient function\sub summation of
150: unit fractions
151: Euclid\sub numbers
151: Mersenne\sub numbers
151: Peirce\sub sequence
151: fractions\sub unreduced
151: phi function\sub divisibility by
151: squarefree
151: totient function\sub divisibility by
152: Farey\sub distribution of
152: uniformity, deviation from
153--242: binomial coefficients
153: binomial coefficients\sub combinatorial interpretation
153: combinations
153: counting\sub combinations
154: binomial coefficients\sub definition
154: binomial coefficients\sub indices of
154: lower index of binomial coefficient
154: notation\sub extension of
154: traps
154: upper index of binomial coefficient
155--156: Pascal's triangle\sub hexagon property
155--156: hexagon property
155: Pascal's triangle
155: Pascal, Blaise
155: Tartaglia, Nicol\`o, triangle
155: small cases
155: triangular numbers
156--157: symmetry identities\sub for binomial coefficients
156: Pascal
156: factorial expansion of binomial coefficients
157--158: absorption identities
157: sandwiching
157: traps
158--159: addition formula for ${n\choose k}_{\mathstrut}$
158--159: binomial coefficients\sub addition formula
158: binomial coefficients\sub combinatorial interpretation
158: cheating\sub not
158: eggs
158: polynomial argument
158: polynomials\sub degree of
159--160: recurrences\sub unfolding
159--160: unfolding a recurrence
159: boundary conditions on sums\sub made easier
159: parallel summation
159: summation\sub parallel
159: zero
160--161: summation\sub on the upper index
160--161: upper summation
160: binomial coefficients\sub combinatorial interpretation
161: indefinite summation\sub of binomial coefficients
162--163: binomial theorem
162: $0^0$
162: Doyle, Sir Arthur Conan
162: Holmes, Thomas Sherlock Scott
162: Moriarty, James
163: Pascal's triangle\sub row sums
163: Taylor, Brook, series
163: binomial theorem\sub special cases
163: polynomial argument
164--165: negating the upper index
164--165: upper negation
164: Pascal's triangle\sub extended upward
164: mnemonics
164: pneumathics
165--166: Pascal's triangle\sub row sums
165--166: hypergeometric series\sub partial sums of
165: sandwiching
166: clich\'es
166: error function
167: unexpected sum
168: Leibniz
168: multinomial coefficients
168: multinomial theorem
168: trinomial coefficients
168: trinomial theorem
169--170: Vandermonde's convolution
169--170: Vandermonde's convolution\sub combinatorial interpretation
169--170: binomial coefficients\sub combinatorial interpretation
169: Chu Shih-Chieh [= Zh\=u Sh\`{\i}ji\'e]
169: Vandermonde, Alexandre Th\'eophile
170: philosophy
171--172: multinomial coefficients
171: Dougall, John
171: trinomial coefficients
172: Dyson, Freeman John
173: BASIC
173: Dijkstra, Edsger Wybe
173: goto, considered harmful
174: binomial coefficients\sub top ten identities of
174: parallel summation
174: summation\sub parallel
175--176: summation\sub on the upper index
175: Youngman, Henry (= Henny)
175: merging
175: notation\sub ghastly
175: referee
175: sorting\sub merge sort
176: upper summation
179: periodic recurrences
179: perturbation method
179: recurrences\sub periodic
180: squares
180: sums\sub of consecutive squares
181: Catalan numbers\sub in sums
181: difficulty measure for summation
181: philosophy
181: summation\sub difficulty measure for
182: football
183--185: double sums\sub considered useful
183: binary search
183: errors, locating our own
183: interchanging the order of summation
183: summation\sub interchanging the order of
183: symmetry identities\sub for binomial coefficients
183: traps
185: interchanging the order of summation
185: summation\sub interchanging the order of
186--187: halving
186: duplication formulas
186: product of consecutive odd numbers
187--192: difference operator\sub $n$th difference
187: Vandermonde's convolution\sub with half-integers
187: binomial coefficients\sub middle
188--189: binomial coefficients\sub reciprocal of
188: $E$: shift operator
188: falling factorial powers\sub difference of
188: falling factorial powers\sub negative
188: negative factorial powers
188: operators\sub equations of
188: shift operator\sub binomial theorems for
189--191: polynomials\sub Newton series for
189--192: Newton\sub series
189: Newton, Sir Isaac
189: partial fraction expansions\sub of $1/x{x+n\choose n}$
189: polynomials
191--192: interpolation
191: $E$: shift operator
191: Taylor
191: operators\sub equations of
191: shift operator\sub binomial theorems for
192--196: inversion formulas\sub for binomial coefficients
192: Stirling, James
192: factorial function\sub generalized to nonintegers
192: generalized factorial function
193--194: recurrences\sub implicit
193--195: implicit recurrences
193--196: counting\sub derangements
193--196: football victory problem
193--196: permutations\sub fixed points in
193: fans
193: inversion formulas
194--196: derangements
194--196: subfactorial
194--200: $\?$: subfactorial
194: philosophy
195--196: triangular numbers
195: Boggs, Wade Anthony
195: Cobb, Tyrus Raymond
195: Stirling
195: baseball
195: cheating
195: lies, and statistics
195: nearest integer\sub rounding to
195: probability
195: radix notation
195: rounding to nearest integer
196--204: generating functions
196: analytic functions
196: holomorphic functions
196: power series
197: bracket notation\sub for coefficients
197: coefficient extraction
197: convolution
197: generating functions\sub for convolutions
198: Vandermonde's convolution\sub derived from generating functions
199--200: counting\sub derangements
199--200: derangements\sub generating function
199--200: football victory problem
199: binomial theorem\sub special cases
200--202: exponential series, generalized
200--202: generalized exponential series
200--204: binomial series, generalized
200--204: generalized binomial series
201--202: Vandermonde's convolution\sub generalized
201: Lambert, Johann Heinrich
202: Eisenstein, Ferdinand Gotthold Max
202: Euler
202: convolution\sub identities for
203: Catalan numbers
203: Catalan numbers\sub in sums
203: Catalan numbers\sub table of
203: Catalan, Eug\`ene Charles
204--223: hypergeometric series
204: complex numbers\sub roots of unity
204: roots of unity
205--206: geometric progression\sub generalized
205: Euler
205: Gau{\ss} (= Gauss)
205: Riemann, Georg Friedrich Bernhard
205: argument of hypergeometric
205: lower parameters of hypergeometric series
205: upper parameters of hypergeometric series
206: Bessel, Friedrich Wilhelm, functions
206: Kummer, Ernst Eduard
206: binomial theorem\sub as hypergeometric series
206: confluent hypergeometric series
206: convergence\sub of power series
206: formal power series
206: hypergeometric series\sub confluent
206: power series\sub formal
207--208: rational functions
207--209: term ratio
207: Euler
207: Fundamental Theorem of Algebra
207: Gau{\ss} (= Gauss)
207: Gau{\ss} (= Gauss)\sub hypergeometric series
207: Pfaff, Johann Friedrich
207: Sawyer, Walter Warwick
207: hypergeometric series\sub Gaussian
208--210: parallel summation
208--210: summation\sub parallel
209--210: degenerate hypergeometric series
209--210: hypergeometric series\sub degenerate
210--211: factorial function\sub generalized to nonintegers
210--211: generalized factorial function
210--211: notation\sub extension of
210--214: Gamma function
210: Euler
210: Stirling
210: polynomial argument\sub opposite of
211--212: term ratio
211--213: Vandermonde's convolution\sub as a hypergeometric series
211: binomial coefficients\sub definition
211: binomial coefficients\sub generalized
211: complex factorial powers
211: duality\sub between factorial and Gamma functions
211: factorial expansion of binomial coefficients
211: falling factorial powers\sub complex
211: generalized binomial coefficients
211: lower index of binomial coefficient\sub complex valued
211: rising factorial powers\sub complex
212: $\Re$: real part
212: Gau{\ss} (= Gauss)
212: real part
213--214: factorial function\sub generalized to nonintegers
213--214: generalized factorial function
213: Kummer\sub formula for hypergeometrics
214--215: Saalsch\"utz\sub identity
214: Dixon\sub formula
214: Pfaff
214: Saalsch\"utz, Louis
215--216: unexpected sum
215: Andrews, George W. Eyre
216--223: hypergeometric series\sub transformations of
216: degenerate hypergeometric series
216: hypergeometric series\sub degenerate
217: Kummer\sub formula for hypergeometrics
217: Pfaff
217: Pfaff\sub reflection law
217: reflection law for hypergeometrics
218--219: Vandermonde's convolution\sub generalized
219--221: $\vartheta$
219--221: derivative operator\sub with hypergeometric series
219--221: hypergeometric series\sub differential equation for
219--221: theta operator
219: \TeX
219: operators\sub theta ($\vartheta$)
220: puns
221: binomial theorem\sub as hypergeometric series
222: Gau{\ss} (= Gauss)\sub identity for hypergeometrics
222: degenerate hypergeometric series
222: hypergeometric series\sub degenerate
222: traps
223--224: indefinite summation\sub of binomial coefficients
223--230: hypergeometric series\sub partial sums of
223: Bailey, Wilfrid Norman
223: Gasper, George, Jr.
223: Rahman, Mizanur
223: reference books
223: useless identity
224--225: term ratio
224--226: rational functions
224--227: Gosper\sub algorithm
224--227: algorithms\sub Gosper's
224--229: indefinite summation\sub of hypergeometric terms
224--229: summation\sub in hypergeometric terms
224: Gosper, Ralph William, Jr.
224: hypergeometric series\sub partial sums of
224: hypergeometric terms
224: term\sub hypergeometric
225: divisibility\sub of polynomials
225: polynomials\sub divisibility of
226: deg
226: polynomials\sub degree of
227--229: Gosper\sub algorithm, examples
228--229: Doyle
228--229: Holmes
229--231: Zeilberger
229--241: Gosper-Zeilberger algorithm
229--241: algorithms\sub Gosper-Zeilberger
229--241: summation\sub definite
229--241: summation\sub mechanical
229: Petkov\v{s}ek, Marko
229: Watson, John Hamish
230--233: binomial theorem\sub discovered mechanically
230: thinking\sub not at all
232: deg
232: telescoping
233: Gosper-Zeilberger algorithm\sub summary
234--235: Saalsch\"utz\sub identity
234--235: perspiration
234: Vandermonde's convolution\sub derived mechanically
234: art and science
234: science and art
235: leading coefficient
236: summation\sub factors
236: telescoping
236: unexpected sum
238--239: Ap\'ery\sub numbers
238: Ap\'ery, Roger
238: Cohen, Henri Jos\'e
238: Riemann's zeta function\sub evaluated at integers
238: Zagier, Don Bernard
238: Zeilberger
238: irrational numbers
238: zeta function\sub evaluated at integers
239--241: proper terms
239: Dyson
239: Littlewood, John Edensor
239: homogeneous linear equations
240: Wilf
240: Zeilberger
240: base term
240: linear difference operators
240: operators\sub shift ($E$, $K$, $N$)
240: shift operator
241: $\Delta$: difference operator
241: Wilf
241: Zeilberger
241: difference operator
241: operators\sub equations of
242: Pascal's triangle\sub hexagon property
242: exponential series
242: generalized exponential series
242: hexagon property
243: Pascal's triangle\sub row products
243: binomial series
243: bloopergeometric series
243: generalized binomial series
243: hyperfactorial
243: hypergeometric terms
243: superfactorials
243: term\sub hypergeometric
244: $\pi$ ($\approx3.14159$)
244: Euler\sub identity for hypergeometrics
244: duplication formulas
244: factorial function\sub duplication formula
245: $\sum$-notation
245: Gosper\sub algorithm, examples
245: Sigma-notation\sub ambiguity of
245: ambiguous notation
245: binomial number system
245: binomial theorem\sub for factorial powers
245: carries\sub in divisibility of $m+n\choose m$
245: confluent hypergeometric series
245: divides exactly\sub in binomial coefficients
245: exactly divides\sub in binomial coefficients
245: falling factorial powers\sub binomial theorem for
245: hypergeometric series\sub confluent
245: hypergeometric series\sub partial sums of
245: hypergeometric terms
245: number system\sub binomial
245: radix notation\sub related to prime factors
245: rising factorial powers\sub binomial theorem for
245: squares
245: sums\sub of consecutive squares
245: term\sub hypergeometric