bib.tex

Concrete_Mathematics_2nd_Ed_TeX_Source_Code

Universitet\t{\i}e\/ \bf4},2 (1882), 93--98. Reprinted in his
{\sl Polnoe Sobranie Sochineni\u\i}, volume~3, 128--131. \ French translation,
``Sur les expressions approximatives des int\'egrales d\'efinies par les autres
prises entre les m\^emes limites,'' 
in his {\sl \OE uvres}, volume~2, 716--719.

\bib|chung-graham|%
Fan "Chung" and Ron "Graham", ``On digraph polynomials,''
submitted for publication, 1993.

\bib|clausen1|%
Th.\ "Clausen", ``Ueber die F\"alle, wenn die Reihe von der Form
\begindisplay \def\\{\mskip1mu.\mskip1mu}
y=1+{\alpha\over1}\cdt{\beta\over\gamma}\,x+
    {\alpha\\\alpha+1\over1\\2}\cdt{\beta\\\beta+1\over\gamma\\\gamma+1}\,x^2
   +\vcenter{\hbox{$\scriptstyle\rm etc.$}}
\enddisplay
ein Quadrat von der Form
\begindisplay \def\\{\mskip1mu.\mskip1mu}
z=1+{\alpha'\over1}\cdt{\beta'\over\gamma'}\cdt{\delta'\over\epsilon'}\,x+
    {\alpha'\!\\\alpha'{+}1\over1\\2}\cdt
      {\beta'\!\\\beta'{+}1\over\gamma'\!\\\gamma'{+}1}
    \cdt{\delta'\!\\\delta'{+}1\over\epsilon'\!\\\epsilon'{+}1}\,x^2
   +\vcenter{\hbox{$\scriptstyle\rm etc.$}}\hbox{ \ hat,''}
\enddisplay
{\sl Journal f\"ur die reine und angewandte Mathematik\/ \bf3} (1828), 89--91.

\bib|clausen2|%
Th.\ "Clausen", ``Beitrag zur Theorie der Reihen,''
{\sl Journal f\"ur die reine und angewandte Mathematik\/ \bf3} (1828), 92--95.

\bib|clausen3|%
Th.\ "Clausen", ``Theorem,'' {\sl Astronomische Nachrichten\/ \bf17}
(1840), col\-umns 351--352.

\bib|carroll-pictures|%
Stuart Dodgson "Collingwood", {\sl The Lewis "Carroll" Picture Book}. \
T. Fisher Unwin, 1899. Reprinted by Dover, 1961, with the new title
{\sl Diversions and Digressions of Lewis Carroll.}

\bib|comtet|%
Louis "Comtet", {\sl Advanced Combinatorics}. \
Dordrecht, Reidel, 1974.

\bib|conway-graham|%
J.\,H. "Conway" and R.\,L. "Graham", ``Problem E\,2567: A periodic
recurrence,'' {\sl American Mathematical Monthly\/ \bf84} (1977), 570--571.

\bib|cramer|%
Harald "Cram\'er", ``On the order of magnitude of the difference
between consecutive prime numbers,''
{\sl Acta Arithmetica\/ \bf2} (1937), 23--46.

\bib|crelle|%
A.\,L. "Crelle", ``D\'emonstration \'el\'ementaire du th\'eor\`eme de
"Wilson" g\'en\'e\-ralis\'e,''
{\sl Journal f\"ur die reine und angewandte Mathematik\/ \bf20} (1840), 29--56.

\bib|crowe|%
D.\,W. "Crowe", ``The $n$-dimensional cube and the Tower of Hanoi,''
{\sl American Mathematical Monthly\/ \bf63} (1956), 29--30.

\bib|csirik|%
J\'anos A. "Csirik", ``Optimal strategy for the first player in the Penney
ante game,'' {\sl Combinatorics, Probability and Computing\/ \bf1} (1992),
311--321.

\bib|curtiss|%
D.\,R. "Curtiss", ``On "Kellogg"'s Diophantine problem,''
{\sl American Mathematical Monthly\/ \bf29} (1922), 380--387.

\bib|david-barton|%
F.\,N. "David" and D.\,E. "Barton", {\sl Combinatorial Chance}. \
Hafner, 1962.

\bib|davis|%
Philip J. "Davis", ``Leonhard "Euler"'s integral: A historical profile
of the "Gamma function",'' {\sl American Mathematical Monthly\/ \bf66}
(1959), 849--869.

\bib|davison|%
J.\,L. "Davison", ``A series and its associated continued fraction,''
{\sl Proceedings of the American Mathematical Society\/ \bf63}
(1977), 29--32.

\bib|de-bruijn|%
N.\,G. "de Bruijn", {\sl Asymptotic Methods in Analysis}. \
North-Holland, 1958; third edition, 1970. Reprinted by Dover, 1981.

\bib|de-br-prob9|%
N.\,G. "de Bruijn", ``Problem 9,'' {\sl Nieuw Archief voor Wiskunde},
series 3, {\bf12} (1964), 68.

\bib|de-moivre|%
Abraham "de Moivre", {\sl Miscellanea analytica de seriebus et quadraturis}. \
London, 1730.

\bib|dedekind|%
R. "Dedekind", ``Abri\ss\ einer Theorie der h\"oheren Congruenzen in
Bezug auf einen reellen Primzahl-Modulus,''
{\sl Journal f\"ur die reine und angewandte Mathematik\/ \bf54} (1857),
1--26. Reprinted in his {\sl Gesammelte mathematische Werke}, volume~1, 40--67.

\bib|dickson|%
Leonard Eugene "Dickson", {\sl History of the Theory of Numbers}. \
Carnegie Institution of Washington, volume~1, 1919; volume~2, 1920;
volume~3, 1923. Reprinted by Stechert, 1934, and by Chelsea, 1952, 1971.

\bib|dijkstra|%
Edsger W. "Dijkstra", {\sl Selected Writings on Computing: A Personal
Perspective}. \ Springer-Verlag, 1982.

\bib|dirichlet-schubfach|%
G. Lejeune "Dirichlet", ``Verallgemeinerung eines Satzes aus der Lehre
von den Kettenbr\"uchen nebst einigen Anwendungen auf die Theorie der
Zahlen,'' {\sl Bericht \"uber die Verhandlungen der K\"oniglich-Preu\ss ischen
Akademie der Wissenschaften zu Berlin\/} (1842), 93--95. Reprinted in
his {\sl Werke}, volume~1, 635--638.

\bib|dixon|%
A.\,C. "Dixon", ``On the sum of the cubes of the coefficients in a
certain expansion by the binomial theorem,'' {\sl Messenger of
Mathematics\/ \bf20} (1891), 79--80.

\bib|dougall|%
John "Dougall", ``On Vandermonde's theorem, and some more general expansions,''
{\sl Proceedings of the Edinburgh Mathematical Society\/ \bf25} (1907),
114--132.

\bib|holmes-four|%
A. Conan "Doyle", ``The sign of the four; or, The problem of the Sholtos,''
{\sl Lippincott's Monthly Magazine\/} (Philadelphia) {\bf45} (1890),
147--223.

\bib|holmes-final|%
A. Conan "Doyle", ``The adventure of the final problem,''
{\sl The Strand Magazine\/ \bf6} (1893), 558--570.

\bib|du-bois|%
P. du "Bois-Reymond", ``Sur la grandeur relative des infinis des fonctions,''
{\sl Annali di Matematica pura ed applicata}, series 2, {\bf4} (1871), 338--353.

\bib|dubner|%
Harvey "Dubner", ``Generalized repunit primes,''
{\sl Mathematics of Computation\/ \bf61} (1993), 927--930.

\bib|dudeney|%
Henry Ernest "Dudeney", {\sl The Canterbury Puzzles and Other Curious Problems}. \
E.\,P. Dutton, New~York, 1908; 4th edition, Dover, 1958.
\ (Dudeney had first considered the generalized Tower of Hanoi in {\sl The
Weekly Dispatch}, on 25 May 1902 and 15 March 1903.)

\bib|gauss-bio|%
G. Waldo "Dunnington", {\sl Carl Friedrich "Gauss": Titan of Science}. \
 Exposition Press, New York, 1955.

\bib|dyson|%
F.\,J. "Dyson", ``Some guesses in the theory of partitions,'' {\sl Eureka\/
\bf8} (1944), 10--15.

\bib|edwards|%
A.\,W.\,F. "Edwards", {\sl Pascal's Arithmetical Triangle}. \
Oxford University Press, 1987.

\bib|eisenstein-exp|%
G. "Eisenstein", ``Entwicklung von $\smash{
 \alpha^{\alpha^{\alpha^{^{.^{.^.}}}}}}\!$,''
{\sl Journal f\"ur die reine und angewandte Mathematik\/ \bf28}
(1844), 49--52. Reprinted in his {\sl Mathematische Werke\/ \bf1}, 122--125.

\bib|elkies|%
Noam D. "Elkies", ``On $A^4+B^4+C^4=D^4$,'' {\sl Mathematics of Computation\/
\bf 51} (1988), 825--835.

\bib|erdos-curtiss|%
"Erd\H os" P\'al, ``Az $\displaystyle{1\over x_1}
+{1\over x_2}+\cdots+{1\over x_{n_{\mathstrut}}}={a\over b}$
 egyenlet eg\'esz sz\'am\'u
meg\-old\'asair\'ol,'' % that journal did hyphenate after the g!
{\sl Matematikai Lapok\/ \bf1} (1950), 192--209. English abstract on page~210.

\bib|erdos-scottish|%
Paul "Erd\H os", ``My Scottish Book `problems','' in {\sl The Scottish Book:
Mathematics from the Scottish Caf\'e\/},
edited by R.~Daniel "Mauldin", 1981, \hbox{35--45}.

\bib|erdos-graham|%
P. "Erd\H os" and R.\,L. "Graham", {\sl Old and New Problems and Results in
Combinatorial Number Theory}. \ Universit\'e de Gen\`eve, L'Enseignement
Math\'ematique, 1980.

\bib|ruzsa-et-al|%
P. "Erd\H os", R.\,L. "Graham", I.\,Z. "Ruzsa", and E.\,G. "Straus", ``On the
prime factors of $2n\choose n$,''
{\sl Mathematics of Computation\/ \bf29} (1975), 83--92.

\bib|esw-levine|%
Arulappah "Eswarathasan" and Eugene "Levine", ``$p$-integral harmonic sums,''
{\sl Discrete Mathematics\/ \bf91} (1991), 249--257.

\bib|euclid-elts|% 0Gmm 1Dlt 2Tht 3Lmb 4Xi 5Pi 6Sgm 7Ups 8Phi 9Psi 10Omg
"Euclid", {\sl @6TOI#+XEIA}.
 \ Ancient manuscript first printed in Basel, 1533.
Scholarly edition (Greek and Latin) by J.\,L. "Heiberg" in five volumes,
Teubner, Leipzig, 1883--1888.

\bib|euler-factorial|% E788 (Enestrom index no., JhrsbchtDMV 1910, Erg_band 4)
Leonhard "Euler", letter to Christian "Goldbach" (13~October 1729), in
{\sl Correspondance Math\'ematique et Physique de Quelques C\'el\`ebres
G\'eom\`etres du XVIII\kern1pt\raise.2ex\hbox{\`eme} Si\`ecle},
 edited by P.\,H. "Fuss", St.~Petersburg, 1843, volume~1, 3--7.
% this letter is number 715 in the index volume for Euler's series 4

\bib|euler-gamma|% E19
L. "Euler"o, ``De progressionibus transcendentibus seu quarum termini
generales algebraice dari nequeunt,''
{\sl Commentarii academ\-i{\ae} scientiarum imperialis Petropolitan{\ae}
\bf5} (1730), 36--57.
Re\-printed in his {\sl Opera Omnia}, series~1, volume~14, 1--24.

\bib|euler-summation|% E25
Leonh.~"Euler"o, ``Methodus generalis summandi progressiones,''
{\sl Commentarii academ\-i{\ae} scientiarum imperialis Petropolitan{\ae}
\bf6} (1732), 68--97.
Re\-printed in his {\sl Opera Omnia}, series~1, volume~14, 42--72.

\bib|euler-f5|% E26
Leonh.~"Euler"o, ``Observationes de theoremate quodam Fermatiano, aliisque
ad numeros primos spectantibus,''
{\sl Commentarii academ\-i{\ae} scientiarum imperialis Petropolitan{\ae}
\bf6} (1732), 103--107.
Re\-printed in his {\sl Opera Omnia}, series~1, volume~2, 1--5.
Reprinted in his {\sl Commentationes arithmetic{\ae} collect{\ae}},
volume~1, 1--3.

\bib|euler-harmonics|% E43
Leonh.~"Euler"o, ``De progressionibus harmonicis observationes,''
{\sl Commentarii academ\-i{\ae} scientiarum imperialis Petropolitan{\ae}
\bf7} (1734), 150--161.
Re\-printed in his {\sl Opera Omnia}, series~1, volume~14, 87--100.

\bib|euler-eulerian|% E55
Leonh.~"Euler"o, ``Methodus universalis series summandi ulterius promota,''
{\sl Commentarii academ\-i{\ae} scientiarum imperialis Petropolitan{\ae}
\bf8} (1736), 147--158.
Re\-printed in his {\sl Opera Omnia}, series~1, volume~14, 124--137.

\bib|euler-e-cf|% E71 (not Eulero this time)
Leonh.~"Euler", ``De fractionibus continuis, Dissertatio,''
{\sl Commentarii academ\-i{\ae} scientiarum imperialis Petropolitan{\ae}
\bf9} (1737), 98--137.
Reprinted in his {\sl Opera Omnia}, series~1, volume~14, 187--215.

\bib|euler-goof|% E72
Leonh.~"Euler", ``Vari{\ae} observationes circa series infinitas,''
{\sl Commentarii academ\-i{\ae} scientiarum imperialis Petropolitan{\ae}
\bf9} (1737), 160--188.
Reprinted in his {\sl Opera Omnia}, series~1, volume~14, 216--244.

\bib|euler-fourier|% E788
Leonhard "Euler", letter to Christian "Goldbach" (4~July 1744), in
{\sl Correspondance Math\'ematique et Physique de Quelques C\'el\`ebres
G\'eom\`etres du XVIII\kern1pt\raise.2ex\hbox{\`eme} Si\`ecle},
 edited by P.\,H. "Fuss", St.~Petersburg, 1843, volume~1, 278--293.
% this letter is number 794 in the index volume for Euler's series 4

\bib|euler-intro-anal|% E101
Leonhardo "Euler"o, {\sl Introductio in Analysin Infinitorum}. \
Tomus primus, Lausanne, 1748.
Reprinted in his {\sl Opera Omnia}, series~1, volume 8.
Translated into French, 1786; German, 1788; Russian, 1936.

\bib|euler-partitions|% E191
L. "Euler"o, ``De partitione numerorum,''
{\sl Novi commentarii academ\-i{\ae} scientiarum imperialis Petropolitan{\ae}
\bf3} (1750), 125--169.
Reprinted in his {\sl Commentationes arithmetic{\ae} collect{\ae}},
volume~1, 73--101.
Reprinted in his {\sl Opera Omnia}, series~1, volume~2, 254--294.

\bib|euler-diff-calc|% E212
Leonhardo "Euler"o, {\sl Institutiones Calculi Differentialis cum eius usu
in An\-al\-ysi Finitorum ac Doctrina Serierum}. \
Berlin, Academi{\ae} Imperialis Scientiarum Petropolitan\ae, 1755.
Reprinted in his {\sl Opera Omnia}, series~1, volume~10.
Translated into German, 1790.

\bib|euler-totient|% E271
L. "Euler"o, ``Theoremata arithmetica nova methodo demonstrata,''
{\sl Novi commentarii academi{\ae} scientiarum imperialis Petropolitan{\ae}
\bf8} (1760), 74--104.
(Also presented in 1758 to the Berlin Academy.)
Reprinted in his {\sl Commentationes arithmetic{\ae} collect{\ae}},
volume~1, 274--286.
Reprinted in his {\sl Opera Omnia}, series~1, volume~2, 531--555.

\bib|euler-continuants|% E281
L. "Euler"o, ``Specimen algorithmi singularis,''
{\sl Novi commentarii academ\-i{\ae} scientiarum imperialis Petropolitan{\ae}
\bf9} (1762), 53--69.
(Also presented in 1757 to the Berlin Academy.)
Reprinted in his {\sl Opera Omnia}, series~1, volume~15, 31--49.

\bib|euler-middle|% E326
L. "Euler"o, ``Observationes analytic\ae,''
{\sl Novi commentarii academi{\ae} scientiarum imperialis
Petropolitan{\ae}
\bf11} (1765), 124--143.
Reprinted in his {\sl Opera Omnia}, series~1, volume~15, 50--69.

\bib|euler-algebra|% E387
Leonhard "Euler", {\sl Vollst\"andige Anleitung zur Algebra.
Erster Theil. Von den verschiedenen Rechnungs-Arten,
Verh\"altnissen und Proportionen}. \
St.~Petersburg, 1770.
Reprinted in his {\sl Opera Omnia}, series~1, volume~1.
Translated into Russian, 1768;
Dutch, 1773; French, 1774; Latin, 1790; English, 1797.

\bib|euler-conject|% E428
L. "Euler"o, ``Observationes circa bina biquadrata quorum summam in duo
alia biquadrata resolvere liceat,''
{\sl Novi commentarii academi{\ae} scientiarum imperialis Petropolitan{\ae}
\bf17} (1772), 64--69.
Reprinted in his {\sl Commentationes arithmetic{\ae} collect{\ae}},
volume~1, 473--476.
Reprinted in his {\sl Opera Omnia}, series~1, volume~3, 211--217.

\bib|euler-josephus|% E476
L. "Euler"o, ``Observationes circa novum et singulare progressionum
genus,''
{\sl Novi commentarii academi{\ae} scientiarum imperialis Petropolitan{\ae}
\bf20} (1775), 123--139.
Reprinted in his {\sl Opera Omnia}, series~1, volume~7, 246--261.

\bib|euler-lambert|% E532
L. "Euler"o, ``De serie "Lambert"ina, plurimisque eius insignibus
proprietatibus,'' {\sl Acta academi{\ae} scientiarum imperialis
Petropolitan{\ae}\/ \bf3},2 (1779), 29--51.
Reprinted in his {\sl Opera Omnia}, series~1, volume~6, 350--369.

\bib|euler-hyp|% E710
L. "Euler"o, ``Specimen transformationis singularis serierum,''
{\sl Nova acta academi{\ae} scientiarum imperialis Petropolitan{\ae}
\bf12} (1794), 58--70.