bib.tex

Concrete_Mathematics_2nd_Ed_TeX_Source_Code

% Bibliography for Concrete Mathematics
% (c) Addison-Wesley, all rights reserved.
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\beginchapter B Bibliography

HERE ARE THE WORKS cited in this book. Numbers in the margin specify the
page numbers where citations occur.
\g\noindent\llap{``}This paper fills a much-needed gap in~the literature.''\par
\hfill\dash---Math.\thinspace Reviews\g

References to published problems are generally made to the places where
solutions can be found, instead of to the original problem statements.

Wherever possible, names and titles are spelled here as they appeared in
the original publication.

\hyphenation{re-printed Leip-zig Mathe-matik}
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\openin\bnxi=bnx % bnx.tex should contain all the .bnx files
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% and it should be numerically sorted and followed by the line `[999] 0.'
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  \docites \ifnum\hits>0 .\fi\g}
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\bib|abel|%
N.\,H. "Abel", letter to B. "Holmboe" (1823), in his {\sl \OE uvres
Com\-pl\`etes}, first edition, 1839, volume~2, 264--265.
Reprinted in the second edition, 1881, volume~2, 254--255.

\bib|abramowitz-stegun|%
Milton "Abramowitz" and Irene A. "Stegun", editors, {\sl Handbook of
Mathematical Functions}. \
 United States Government Printing Office, 1964.
 Reprinted by Dover, 1965.

\bib|adams-davison|%
William W. "Adams" and J.\,L. "Davison",
 ``A remarkable class of continued fractions,''
{\sl Proceedings of the American Mathematical Society\/ \bf65}
(1977), 194--198.

\bib|aho-sloane|%
A.\,V. "Aho" and N.\,J.\,A. "Sloane",
 ``Some doubly exponential sequences,''
{\sl Fibonacci Quarterly\/ \bf11} (1973), 429--437.

\bib|ahrens|%
W. "Ahrens", {\sl Mathematische Unterhaltungen und Spiele}. \
Teubner, Leipzig, 1901.
Second edition, in two volumes, 1910 and 1918.

\bib|akhiezer|%
Naum Il'ich "Akhiezer", {\sl Klassicheska\t\i a Problema Momentov i Nekotorye
Voprosy Analiza, Sv\t\i azannye s Ne\t\i u}. \ Moscow, 1961.
English translation, {\sl The Classical Moment Problem and Some Related Questions
in Analysis},
Hafner, 1965.

\bib|allardice|%
R.\,E. "Allardice" and A.\,Y. "Fraser",
 ``La Tour d'Hano\"\i,''
{\sl Proceedings of the Edinburgh Mathematical Society\/ \bf2} (1884), 50--53.

\bib|andre|%
D\'esir\'e "Andr\'e", ``Sur les permutations altern\'ees,''
{\sl Journal de Math\'ema\-tiques pures et appliqu\'ees}, series 3, {\bf7}
(1881), 167--184.

\bib|andrews-siam|%
George E. "Andrews", ``Applications of basic hypergeometric functions,''
{\sl SIAM Review\/ \bf16} (1974), 441--484.

\bib|andrews-saalschutz|%
George E. "Andrews", ``On sorting two ordered sets,''
{\sl Discrete Mathematics\/ \bf11} (1975), 97--106.

\bib|andrews-partitions|%
George E. "Andrews", {\sl The Theory of Partitions}. \ Addison-Wesley, 1976.

\bib|andrews-euler|%
George E. "Andrews", ``Euler's `exemplum memorabile inductionis
fallacis' and $q$-trinomial coefficients,'' {\sl Journal of the
American Mathematical Society\/ \bf3} (1990), 653--669.

\bib|andrews-uchimura|%
George E. "Andrews" and K. "Uchimura", ``Identities in combinatorics IV:
Differentiation and harmonic numbers,'' {\sl Utilitas Mathematica\/ \bf28}
(1985), 265--269.

\bib|apery|%
Roger "Ap\'ery", ``Interpolation de fractions continues et irrationalit\'e
de certaines constantes,'' in {\sl Math\'ematiques}, Minist\`ere
des universit\'es (France), Comit\'e
des travaux historiques et scientifiques, Section des sciences,
{\sl Bulletin de la Section des Sciences\/ \bf3} (1981), 37--53.

\bib|arnold|%
V.\,I. "Arnold", ``Bernoulli-Euler updown numbers associated with function
singularities, their combinatorics and arithmetics,'' {\sl Duke
Mathematical Journal\/ \bf63} (1991), 537--555.

\bib|atkinson|%
M.\,D. "Atkinson", ``The cyclic towers of Hanoi,''
{\sl Information Processing Letters\/ \bf13} (1981), 118--119.

\bib|bachmann|%
Paul "Bachmann", {\sl Die analytische Zahlentheorie}. \
Teubner, Leipzig, 1894.

\bib|bailey|%
W.\,N. "Bailey", {\sl Generalized Hypergeometric Series.} \
Cambridge University Press, 1935; second edition, 1964.

\bib|bailey-jacobi|%
W.\,N. "Bailey", ``The generating function for "Jacobi polynomials",''
{\sl Journal of the London Mathematical Society\/ \bf13} (1938), 243--246.

\bib|rouse-ball|%
W.\,W. Rouse "Ball" and H.\,S.\,M. "Coxeter",
{\sl Mathematical Recreations and Essays}, twelfth edition. \
University of Toronto Press, 1974.
\ (A revision of Ball's {\sl Mathematical Recreations and Problems},
first published by Macmillan, 1892.)

\bib|barlow|%
P. "Barlow", ``Demonstration of a curious numerical proposition,''
{\sl Journal of Natural Philosophy, Chemistry, and the Arts\/ \bf27}
(1810), 193--205.

\bib|beatty|%
Samuel "Beatty", ``Problem 3177,'' {\sl American Mathematical Monthly\/
\bf 34} (1927), 159--160.

\bib|bell-gf|%
E.\,T. "Bell", ``"Euler" algebra,''
{\sl Transactions of the American Mathematical Society\/ \bf25} (1923),
 135--154.

\bib|bell-numbers|%
E.\,T. "Bell", ``Exponential numbers,''
{\sl American Mathematical Monthly\/ \bf41} (1934), 411--419.

\bib|bender|%
Edward A. "Bender", ``Asymptotic methods in enumeration,''
{\sl SIAM Review\/ \bf16} (1974), 485--515.

\bib|bernoulli-ars|%
Jacobi "Bernoulli", {\sl Ars Conjectandi}, opus posthumum.
Basel, 1713. Reprinted in {\sl Die Werke von Jakob Bernoulli}, volume~3,
107--286.

\bib|bertrand|%
J. "Bertrand", ``M\'emoire sur le nombre de valeurs que peut prendre une
fonction quand on y permute les lettres qu'elle renferme,''
{\sl Journal de l'\'Ecole Royale Polytechnique\/ \bf18}, cahier 30 (1845),
123--140.

\bib|crc-tables|%
William H. "Beyer", editor, {\sl CRC Standard Mathematical Tables and
Formulae}, 29th
edition. \ CRC Press, Boca Raton, Florida, 1991.

\bib|bienayme|%
J. "Bienaym\'e", ``Consid\'erations \`a l'appui de la d\'ecouverte de "Laplace"
sur la loi de probabilit\'e dans la m\'ethode des moindres carr\'es,''
{\sl Comptes Rendus hebdomadaires des s\'eances de l'Acad\'emie des Sciences\/}
(Paris) {\bf37} (1853), 309--324.

\bib|binet-det|%
J. "Binet", ``M\'emoire sur un syst\`eme de Formules analytiques, et leur
application \`a des consid\'erations g\'eom\'etriques,''
{\sl Journal de l'\'Ecole Polytechnique\/ \bf9}, cahier 16 (1812),
280--354.

\bib|binet|%
J. "Binet", ``M\'emoire sur l'int\'egration des \'equations lin\'eaires
aux diff\'e\-ren\-ces finies, d'un ordre quelconque, \`a coefficients
variables,'' {\sl Comptes Rendus hebdomadaires des s\'eances
 de l'Acad\'emie des  Sciences\/} (Paris) {\bf17} (1843), 559--567.

\bib|blom|%
Gunnar "Blom", ``Problem E\,3043: Random walk until no shoes,''
{\sl American Mathematical Monthly\/ \bf94} (1987), 78--79.

\bib|boas-wrench|%
R. P. "Boas", Jr.\ and J. W. "Wrench", Jr., ``Partial sums of the harmonic
series,'' {\sl American Mathematical Monthly\/ \bf78} (1971), 864--870.

\bib|bohl|%
P. "Bohl", ``\"Uber ein in der Theorie der s\"akularen St\"orungen vorkommendes
Problem,'' {\sl Journal f\"ur die reine und angewandte Mathematik\/ \bf135}
(1909), 189--283.

\bib|borel|%
\'Emile "Borel", {\sl Le\c cons sur les s\'eries \`a termes positifs}. \
Gauthier-Villars, 1902.

\bib|borweins|%
Jonathan M. "Borwein" and Peter B. "Borwein", {\sl Pi and the AGM}. \
Wiley, 1987.

\bib|brent-gaps|%
Richard P. "Brent", ``The first occurrence of large gaps between
successive primes,'' {\sl Mathematics of Computation\/ \bf27} (1973), 959--963.

\bib|brent-gamma|%
Richard P. "Brent", ``Computation of the regular continued fraction for
Euler's constant,''
{\sl Mathematics of Computation\/ \bf31} (1977), 771--777.

\bib|brillhart|%
John "Brillhart", ``Some miscellaneous factorizations,''
{\sl Mathematics of Computation\/ \bf17} (1963), 447--450.

\bib|brocot|%
Achille "Brocot", ``Calcul des rouages par approximation, nouvelle m\'e\-thode,''
{\sl Revue Chronom\'etrique\/ \bf6} (1860), 186--194.
\ (He also published a 97-page monograph with the same title in 1862.)

\bib|brooke|%
Maxey "Brooke" and C.\,R. "Wall", ``Problem B-14: A little surprise,''
{\sl Fibonacci Quarterly\/ \bf1},\,3 (1963), 80.

\bib|bro-alfred|%
Brother U. "Alfred" ["Brousseau"], ``A mathematician's progress,''
{\sl Mathematics Teacher\/ \bf59} (1966), 722--727.

\bib|mort-brown|%
Morton "Brown", ``Problem 6439: A periodic sequence,''
{\sl American Mathematical Monthly\/ \bf92} (1985), 218.

\bib|not-cited-here|%
T. "Brown", ``Infinite multi-variable subpolynormal Woffles which
\g \vskip-6pt (Such papers aren't cited in this book.)\g
do not satisfy the lower regular $Q$-property (Piffles),''
in {\sl A Collection of 250 Papers on Woffle Theory Dedicated to
R.\,S. "Green" on His 23rd Birthday}.
Cited in A.\,K. "Austin", ``Modern research in mathematics,''
{\sl The Mathematical Gazette\/ \bf51} (1967), 149--150.

\bib|t-c-brown|%
Thomas C. "Brown", ``Problem E\,2619: Squares in a recursive
sequence,'' {\sl American Mathematical Monthly\/ \bf85} (1978), 52--53.

\bib|catalan-history|%
William G. "Brown", ``Historical note on a recurrent combinatorial problem,''
{\sl American Mathematical Monthly\/ \bf72} (1965), 973--977.

\bib|burr-fib|%
S.\,A. "Burr", ``On moduli for which the Fibonacci sequence contains a complete
system of residues,'' {\sl Fibonacci Quarterly\/ \bf9} (1971), 497--504.

\bib|canfield|%
E. Rodney "Canfield", ``On the location of the maximum Stirling number(s)
of the second kind,'' {\sl Studies in Applied Mathematics\/ \bf59}
(1978), 83--93.

\bib|carlitz-max|%
L. "Carlitz", ``The generating function for $\max(n_1,n_2,\cdots,n_k)$,
{\sl Portugaliae Mathematica\/ \bf 21} (1962), 201--207.

\bib|alice-looking|%
Lewis "Carroll" [pseudonym of C.\,L. "Dodgson"],
 {\sl Through the Looking Glass
and What Alice Found There}. Macmillan, 1871.

\bib|cassini|%
Jean-Dominique "Cassini", ``Une nouvelle progression de nombres,''
{\sl Histoire de l'Acad\'emie Royale des Sciences}, Paris, volume~1, 201.
\ (Cassini's work is summarized here as one of the mathematical results
presented to the academy in 1680. This volume was published in 1733.)

\bib|catalan-paper|%
E. "Catalan", ``Note sur une \'Equation aux diff\'erences finies,''
{\sl Journal de Math\'ematiques pures et appliqu\'ees\/ \bf3}
(1838), 508--516.

\bib|cauchy-cours|%
Augustin-Louis "Cauchy",
{\sl Cours d'analyse de l'\'Ecole Royale Polytechnique}. \
Imprimerie Royale, Paris, 1821.
Reprinted in his {\sl \OE uvres Com\-pl\`etes}, series~2, volume~3.

\bib|rhind|%
Arnold Buffum "Chace", {\sl The Rhind Mathematical Papyrus}, volume~1. \
Mathematical Association of America, 1927. \ (Includes an excellent bibliography
of "Egyptian mathematics" by R.\,C. "Archibald".)

\bib|chaimovich-et-al|%
M. "Chaimovich", G. "Freiman", and J. "Sch\"onheim", ``On exceptions
to "Szegedy"'s theorem,'' {\sl Acta Arithmetica\/ \bf49} (1987), 107--112.

\bib|chebyshev|%
P.\,L. Tchebichef ["Chebyshev"], ``M\'emoire sur les nombres premiers,''
{\sl Journal de Math\'e\-ma\-tiques pures et appliqu\'ees\/ \bf17}
(1852), 366--390. Reprinted in his {\sl \OE uvres}, volume~1, 51--70. \
Russian translation, ``O prostykh chislakh,'' in his
{\sl Polnoe Sobranie Sochineni\u\i}, volume~1, 191--207.

\bib|chebyshev-ineq|%
P.\,L. "Chebyshev", ``O srednikh velichinakh,''
{\sl Matematicheski\u\i\ Sbornik'\/ \bf2} (1867), 1--9. Reprinted in his
{\sl Polnoe Sobranie Sochineni\u\i}, volume~2, 431--437. \ French translation,
``Des valeurs moyennes,'' {\sl Journal de Math\'e\-ma\-tiques
pures et appliqu\'ees}, series 2, {\bf12} (1867), 177--184; reprinted
in his {\sl \OE uvres}, volume~1, 685--694.

\bib|chebyshev-mono|%
P.\,L. "Chebyshev", ``O priblizhennykh vyrazheni\t{\i}akh odnikh integralov
cherez drugie, vz\t{\i}atye v tex zhe predelakh,''
{\sl Soobshchen\={\i}\t{\i}a i protokoly zas\t{\i}edan\={\i}\u{\i}
matematicheskago obshchestva pri Imperatorskum\H{} Khar'kovskom\H{}