bib.tex

Concrete_Mathematics_2nd_Ed_TeX_Source_Code

\bib|hillman-hoggatt|%
A.\,P. "Hillman" and V.\,E. "Hoggatt", Jr., ``A proof of Gould's Pascal
hexagon conjecture,'' {\sl Fibonacci Quarterly\/ \bf10} (1972), 565--568, 598.

\bib|hoare|%
C.\,A.\,R. "Hoare", ``Quicksort,''
{\sl The Computer Journal\/ \bf5} (1962), 10--15.

\bib|hsu-identity|%
L.\,C. "Hsu", ``Note on a combinatorial algebraic identity and its application,''
{\sl Fibonacci Quarterly\/ \bf11} (1973), 480--484.

%\bib|inkeri|%
%K. "Inkeri", ``Absch\"atzungen f\"ur eventuelle L\"osungen der Gleichung
%im Fermatschen Problem,'' {\sl Annales Universitatis Turkuensis}, series A,
%{\bf 16}, 1 (1953), 3--9.

\bib|APL|%
Kenneth E. "Iverson", {\sl A Programming Language}. \
Wiley, 1962.

\bib|jacobi|%
C.\,G.\,J. "Jacobi", {\sl Fundamenta nova theori\ae\ functionum ellipticarum}. \
K\"onigsberg, Borntr\"ager, 1829. Reprinted in his {\sl Gesammelte Werke},
volume~1, 49--239.

\bib|bgc|%
Svante "Janson", Donald~E. "Knuth", Tomasz "{\L}uczak", and Boris "Pittel",
``The birth of the giant component,'' {\sl Random Structures and
Algorithms\/ \bf4} (1993), 233--358.

\bib|jarden|%
Dov "Jarden" and Theodor "Motzkin", ``The product of sequences with a common linear
recursion formula of order~2,'' {\sl Riveon Lematematika\/ \bf3} (1949),
25--27, 38 (Hebrew with English summary). English version reprinted in
Dov Jarden, {\sl Recurring Sequences}, Jerusalem, 1958, 42--45; second edition,
1966, 30--33.

\bib|jonassen-knuth|%
Arne "Jonassen" and Donald E. "Knuth", ``A trivial algorithm whose analysis
isn't,'' {\sl Journal of Computer and System Sciences\/ \bf16} (1978),
301--322.

\bib|jones|%
Bush "Jones", ``Note on internal merging,'' {\sl Software\dash---Practice
and Experience\/ \bf2} (1972), 241--243.

\bib|josephus-source|% 0Gmm 1Dlt 2Tht 3Lmb 4Xi 5Pi 6Sgm 7Ups 8Phi 9Psi 10Omg
Flavius "Josephus", {\sl I@6TOPIA IO#-@7#-#-@1#-A\"IKO#-@7#-\ @5O@3EMO#-@7#-\
 @5PO@6 P@{10}\-MAI#+O#-@7#-@6}. \
English translation, {\sl History of the Jewish War against the Romans},
by H.\,St.\,J. "Thackeray",
 in the Loeb Classical Library edition of Josephus's
works, volumes 2 and~3,
Heinemann, London, 1927--1928. \ (The ``Josephus problem'' may be based
on an early manuscript now preserved only in the Slavonic version; see volume~2,
page~xi, and volume~3, page 654.)

\bib|jungen|%
R. "Jungen", ``Sur les s\'eries de Taylor n'ayant que des singularit\'es
alg\'ebrico-logarithmiques sur leur cercle de convergence,''
{\sl Commentarii Mathematici Helvetici\/ \bf3} (1931), 266--306.

\bib|karamata|%
J. "Karamata", ``Th\'eor\`emes sur la sommabilit\'e exponentielle et
d'autres sommabilit\'es rattachant,'' {\sl Mathematica\/} (Cluj) {\bf9}
(1935), 164--178.

\bib|kaucky|%
I. "Kauck\'y", ``Problem E\,2257: A harmonic identity,''
{\sl American Mathematical Monthly\/ \bf78} (1971), 908.

%\bib|kaucky-book|%
%Josef "Kauck\'y", {\sl Kombinatorick\'e Identity.} \
%Bratislava, 1975.

\bib|keiper|%
J.\,B. "Keiper", ``Power series expansions of Riemann's $\xi$ function,''
{\sl Mathematics of Computation\/ \bf58} (1992), 765--773.

\bib|olympiads2|%
Murray S. "Klamkin", {\sl International Mathematical Olympiads, 1978--1985, and
Forty Supplementary Problems}. \ Mathematical Association of America, 1986.

\bib|knoebel|%
R. Arthur "Knoebel", ``Exponentials reiterated,'' {\sl American
Mathematical Monthly\/ \bf88} (1981), 235--252.

\bib|knopp|%
Konrad "Knopp", {\sl Theorie und Anwendung der unendlichen Reihen}. \
Julius Springer, Berlin, 1922; second edition, 1924.
Reprinted by Dover, 1945. Fourth edition, 1947; fifth edition, 1964. English
translation, {\sl Theory and Application of Infinite Series},
1928; second edition, 1951.

\bib|knuth-gamma|%
Donald E. "Knuth", ``Euler's constant to 1271 places,''
{\sl Mathematics of Computation\/ \bf16} (1962), 275--281.

\bib|knuth-trans|%
Donald "Knuth", ``Transcendental numbers based on the Fibonacci
sequence,'' {\sl Fibonacci Quarterly\/ \bf2} (1964), 43--44, 52.

\bib|knuth1|%
Donald E. "Knuth", {\sl The Art of Computer Programming},
volume~1: {\sl Fundamental Algorithms}. \
Addison-Wesley, 1968; second edition, 1973.

\bib|knuth2|%
Donald E. "Knuth", {\sl The Art of Computer Programming},
volume~2: {\sl Semi\-numerical Algorithms}. \
Addison-Wesley, 1969; second edition, 1981.

\bib|knuth3|%
Donald E. "Knuth", {\sl The Art of Computer Programming},
volume~3: {\sl Sorting and Searching}. \
Addison-Wesley, 1973; second printing, 1975.

%\bib|knuth-fib|%
%Donald E. "Knuth", ``Letter to the editor,'' {\sl Fibonacci Quarterly\/ \bf12}
%(1974), 46, 79, 82.

\bib|some-sum|%
Donald E. "Knuth", ``Problem E\,2492: Some sum,''
{\sl American Mathematical Monthly\/ \bf82} (1975), 855.

\bib|mariage-stables|%
Donald E. "Knuth", {\sl Mariages stables et leurs relations avec d'autres
probl\`emes combinatoires}. \
Les Presses de l'Universit\'e de Montr\'eal, 1976. Revised and corrected
edition, 1980.

\bib|texbook|%
Donald E. "Knuth", {\sl The \TeX book}. \ Addison-Wesley, 1984.
Reprinted as volume~A of {\sl Computers \& Typesetting}, 1986.

\bib|knuth-caching|%
Donald E. "Knuth", ``An analysis of optimum caching,''
{\sl Journal of Algorithms\/ \bf6} (1985), 181--199.

\bib|knuthd|%
Donald E. "Knuth", {\sl Computers \& Typesetting}, volume~D:
{\logos METAFONT\kern1pt\sl: The Program}. \
Addison-Wesley, 1986.

\bib|knuth-polya|%
Donald E. "Knuth", ``Problem 1280: Floor function identity,''
{\sl Mathematics Magazine\/ \bf61} (1988), 319--320.

\bib|amm-phi-problem|%
Donald E. "Knuth", ``Problem E\,3106:
A new sum for $n^2$,''
 {\sl American Mathematical Monthly\/ \bf94} (1987), 795--797.

\bib|knuth-fib-mult|%
Donald E. "Knuth", ``Fibonacci multiplication,''
{\sl Applied Mathematics Letters\/ \bf1} (1988), 57--60.

\bib|knuth-fib-composites|%
Donald E. "Knuth", ``A Fibonacci-like sequence of composite numbers,''
 {\sl Mathematics  Magazine\/ \bf63} (1990), 21--25.

\bib|knuth-bci|%
Donald E. "Knuth", ``Problem E\,3309: A binomial coefficient
inequality,''
{\sl American Mathematical Monthly\/ \bf97} (1990), 614.

\bib|knuth-tnn|%
Donald E. "Knuth", ``Two notes on notation,'' {\sl American
Mathematical Monthly\/ \bf99} (1992), 403--422.

\bib|knuth-cp|%
Donald E. "Knuth", ``Convolution polynomials,'' {\sl The Mathematica
Journal\/ \bf2},4 (Fall 1992), 67--78.

\bib|knuth-faul|%
Donald E. "Knuth", ``Johann "Faulhaber" and sums of powers,'' {\sl
Mathematics of Computation\/ \bf 61} (1993), 277--294.

\bib|knuth-bn|%
Donald E. "Knuth", ``Bracket notation for the coefficient-of operator,''
in {\sl A Classical Mind}, essays in honour of C.\,A.\,R.
"Hoare", edited by A.\,W. "Roscoe", Prentice-Hall, 1994, 247--258.

\bib|knuth-buckholtz|%
Donald E. "Knuth" and Thomas J. "Buckholtz", ``Computation of Tangent,
Euler, and Bernoulli numbers,'' "!Euler numbers"
{\sl Mathematics of Computation\/ \bf21} (1967), 663--688.

\bib|knuth-vardi|%
Donald E. "Knuth" and Ilan "Vardi", ``Problem 6581: The asymptotic
expansion of the middle binomial coefficient,'' {\sl American Mathematical
Monthly\/ \bf97} (1990), 626--630.

\bib|kw-carry|%
Donald E. "Knuth" and Herbert S. "Wilf", ``The power of a prime that
divides a generalized binomial coefficient,'' 
{\sl Journal f\"ur die reine und angewandte Mathematik\/ \bf396} (1989),
212--219.

\bib|knuth-zapf|%
Donald E. "Knuth" and Hermann "Zapf", ``AMS Euler\dash---A new typeface
for mathematics,'' {\sl Scholarly Publishing\/ \bf20} (1989), 131--157.

\bib|kramp|%
C. "Kramp", {\sl \'El\'emens d'arithm\'etique universelle}. \
Cologne, 1808.

\bib|kummer|%
E.\,E. "Kummer", ``Ueber die hypergeometrische Reihe
\begindisplay \def\\{\,.\,} \openup2pt
&1+{\alpha\beta\over1\\\gamma}\,x
 +{\alpha(\alpha+1)\beta(\beta+1)\over1\\2\\\gamma(\gamma+1)}\,xx\cr
&\qquad +{\alpha(\alpha+1)(\alpha+2)\beta(\beta+1)(\beta+2)\over
    1\\2\\3\\\gamma(\gamma+1)(\gamma+2)}\,x^3+\ldots\,\hbox{,''}
\enddisplay
{\sl Journal f\"ur die reine und angewandte Mathematik\/ \bf15}
 (1836), 39--83, 127--172. Reprinted in his {\sl Collected Papers},
volume~2, 75--166.

\bib|kummer-carry|%
E.\,E. "Kummer", ``\"Uber die Erg\"anzungss\"atze zu den allgemeinen
Reciprocit\"atsgesetzen,''
{\sl Journal f\"ur die reine und angewandte Mathematik\/ \bf44}
 (1852), 93--146. Reprinted in his {\sl Collected Papers},
 volume~1, 485--538.

\bib|kurshan|%
R.\,P. "Kurshan" and B. "Gopinath", ``Recursively generated periodic sequences,''
{\sl Canadian Journal of Mathematics\/ \bf26} (1974), 1356--1371.

\bib|lagny|%
Thomas Fantet de "Lagny", {\sl Analyse g\'en\'erale ou M\'ethodes nouvelles
pour r\'esoudre les probl\`emes de tous les genres et de tous les
degr\'es \`a l'infini}. \ Published as volume~11 of {\sl M\'emoires
de l'Acad\'emie Royale des Sciences}, Paris, 1733.

\bib|lagrange-wilson|%
de la Grange ["Lagrange"],
``D\'emonstration d'un th\'eor\`eme nouveau concernant
les nombres premiers,''
{\sl Nouveaux M\'emoires de l'Acad\'emie royale des Sciences et
Belles-Lettres}, Berlin (1771), 125--137.
Reprinted in his {\sl \OE uvres}, volume~3, 425--438.

\bib|lagrange-euler|%
de la Grange ["Lagrange"], ``Sur une nouvelle esp\`ece de calcul
 r\'elatif % sic, in the original
\`a la diff\'erentia\-tion \& \`a l'int\'egration des quantit\'es variables,''
{\sl Nouveaux M\'emoires de l'Acad\'emie royale des Sciences et
Belles-Lettres}, Berlin (1772), 185--221.
Reprinted in his {\sl \OE uvres}, volume~3, 441--476.

\bib|lah|%
I. "Lah", ``Eine neue Art von Zahlen, ihre Eigenschaften und Anwendung
in der mathematischen Statistik,'' {\sl Mitteilungsblatt f\"ur
Mathematische Statistik\/ \bf7} (1955), 203--212.

\bib|lamb1|%
I.\,H. "Lambert", ``Observationes vari\ae\ in Mathesin puram,''
{\sl Acta Helvetica\/ \bf3} (1758), 128--168. Reprinted in his
{\sl Opera Mathematica}, volume~1, \hbox{16--51}.

\bib|lamb2|%
"Lambert", ``Observations analytiques,''
{\sl Nouveaux M\'emoires de l'Acad\-\'emie royale des Sciences et
Belles-Lettres}, Berlin (1770), 225--244. Reprinted in his
{\sl Opera Mathematica}, volume~2, 270--290.

\bib|landau-primes|%
Edmund "Landau", {\sl Handbuch der Lehre von der Verteilung der Prim\-zahlen},
two volumes. \
Teubner, Leipzig, 1909.

\bib|landau-vorlesungen|%
Edmund "Landau", {\sl Vorlesungen \"uber Zahlentheorie}, three volumes. \
\kern-.7pt Hirzel, Leipzig, 1927.

\bib|laplace|%
P.\,S. de la Place ["Laplace"], ``M\'emoire sur les approximations
des Formules
qui sont fonctions de tr\`es-grands nombres,'' {\sl M\'emoires de l'Academie
royale des Sciences de Paris\/} (1782), 1--88. Reprinted in his
{\sl \OE uvres Compl\`etes\/ \bf10}, 207--291.

\bib|legendre-theorie|%
Adrien-Marie "Legendre", {\sl Essai sur la Th\'eorie des Nombres}. \
Paris, 1798; second edition, 1808. Third edition (retitled {\sl Th\'eorie
des Nombres}, in two volumes), 1830; fourth edition, Blanchard, 1955.

\bib|lehmer-primality|%
D.\,H. "Lehmer", ``Tests for primality by the converse of Fermat's theorem,''
{\sl Bulletin of the American Mathematical Society}, series~2,
{\bf33} (1927), 327--340. Reprinted in his {\sl Selected Papers}, volume~1,
69--82.

\bib|lehmer-sp|%
D.\,H. "Lehmer", ``On Stern's diatomic series,''
{\sl American Mathematical Monthly\/ \bf36} (1929), 59--67.
% not in his Selected Papers

\bib|lehmer-conj|%
D.\,H. "Lehmer", ``On Euler's totient function,''
{\sl Bulletin of the American Mathematical Society}, series~2,
{\bf38} (1932), 745--751. Reprinted in his {\sl Selected Papers}, volume~1,
319--325.

\bib|leibniz|%
G.\,W. "Leibniz", letter to Johann "Bernoulli" (May 1695), in
{\sl Leibnizens mathematische Schriften}, volume~3, 174--179.

\bib|zeck1|%
C.\,G. "Lekkerkerker", ``Voorstelling van natuurlijke getallen door een som
van getallen van Fibonacci,'' {\sl Simon Stevin\/ \bf29} (1952), 190--195.

\bib|world-series|%
Tam\'as "Lengyel", ``A combinatorial identity and the world series,''
"!baseball"
{\sl SIAM Review\/ \bf35} (1993), 294--297.

\bib|lengyel|%
Tam\'as "Lengyel", ``On some properties of the series $\sum_{k=0}^\infty
k^nx^k$ and the Stirling numbers of the second kind,''
submitted for publication, 1993.

\bib|li-shan-lan|%
"Li" Shan-Lan, {\sl Du\`o J\=\i\ B\u{\i} L\`ei\/} [Sums of Piles Obtained
Inductively]. \ In his {\sl Z\'eg\u{u}x\={\i} Zha\={\i} Su\`anxu\'e\/}
[Classically inspired meditations on mathematics], Nanjing, 1867.

\bib|lieb|%
Elliott H. "Lieb", ``Residual entropy of square ice,''
{\sl Physical Review\/ \bf162} (1967), 162--172.

\bib|liouv|%
J. "Liouville", ``Sur l'expression $\varphi(n)$, qui marque combien la suite
$1$, $2$, $3$, \dots,~$n$ contient de nombres premiers \`a~$n$,''
{\sl Journal de Math\'e\-ma\-tiques pures et appliqu\'ees}, series 2, {\bf2}
(1857), 110--112.

\bib|logan-orth|%
B.\,F. "Logan", ``The recovery of orthogonal polynomials from a sum of squares,''
{\sl SIAM Journal on Mathematical Analysis\/ \bf21} (1990), 1031--1050.

\bib|logan-stirl|%