G. E. Andrews and R. Askey :
“Enumeration of partitions: The role of Eulerian series and \( q \) -orthogonal polynomials ,”
pp. 3–26
in
Higher combinatorics
(West Berlin, 1–10 September 1976 ).
Edited by M. Aigner .
NATO Advanced Study Institutes Series: Series C, Mathematical and Physical Sciences 31 .
Reidel (Dordrecht ),
1977 .
MR
519776
Zbl
0381.10008
incollection
Abstract
People
BibTeX
@incollection {key519776m,
AUTHOR = {Andrews, George E. and Askey, Richard},
TITLE = {Enumeration of partitions: {T}he role
of {E}ulerian series and \$q\$-orthogonal
polynomials},
BOOKTITLE = {Higher combinatorics},
EDITOR = {Aigner, Martin},
SERIES = {NATO Advanced Study Institutes Series:
Series C, Mathematical and Physical
Sciences},
NUMBER = {31},
PUBLISHER = {Reidel},
ADDRESS = {Dordrecht},
YEAR = {1977},
PAGES = {3--26},
DOI = {10.1007/978-94-010-1220-1_1},
NOTE = {(West Berlin, 1--10 September 1976).
MR:519776. Zbl:0381.10008.},
ISSN = {1389-2185},
ISBN = {9789027707956},
}
G. E. Andrews and R. Askey :
“A simple proof of Ramanujan’s summation of the \( {}_1 \psi_1 \) ,”
Aequationes Math.
18 : 3
(1978 ),
pp. 333–337 .
MR
522519
Zbl
0401.33002
article
Abstract
People
BibTeX
A simple proof by functional equations is given for Ramanujan’s \( {}_1 \psi_1 \) sum. Ramanujan’s sum is a useful extension of Jacobi’s triple product formula, and has recently become important in the treatment of certain orthogonal polynomials defined by basic hypergeometric series.
@article {key522519m,
AUTHOR = {Andrews, George E. and Askey, Richard},
TITLE = {A simple proof of {R}amanujan's summation
of the \${}_1 \psi_1\$},
JOURNAL = {Aequationes Math.},
FJOURNAL = {Aequationes Mathematicae},
VOLUME = {18},
NUMBER = {3},
YEAR = {1978},
PAGES = {333--337},
DOI = {10.1007/BF03031684},
NOTE = {MR:522519. Zbl:0401.33002.},
ISSN = {0001-9054},
}
R. Askey :
“Book review: G. E. Andrews, ‘The theory of partitions’ ,”
Bull. Am. Math. Soc. (N.S.)
1 : 1
(1979 ),
pp. 203–210 .
MR
1567111
article
People
BibTeX
@article {key1567111m,
AUTHOR = {Askey, Richard},
TITLE = {Book review: {G}.~{E}. Andrews, ``{T}he
theory of partitions''},
JOURNAL = {Bull. Am. Math. Soc. (N.S.)},
FJOURNAL = {Bulletin of the American Mathematical
Society. New Series},
VOLUME = {1},
NUMBER = {1},
YEAR = {1979},
PAGES = {203--210},
DOI = {10.1090/S0273-0979-1979-14556-7},
NOTE = {MR:1567111.},
ISSN = {0273-0979},
}
G. E. Andrews, R. Askey, and H. Flanders :
“Problems and solutions: Solutions of problems dedicated to Emory P. Starke: S7 ,”
Amer. Math. Monthly
87 : 5
(1980 ),
pp. 403–404 .
MR
1539387
article
People
BibTeX
@article {key1539387m,
AUTHOR = {Andrews, George E. and Askey, Richard
and Flanders, Harley},
TITLE = {Problems and solutions: Solutions of
problems dedicated to {E}mory P. {S}tarke:
{S}7},
JOURNAL = {Amer. Math. Monthly},
FJOURNAL = {American Mathematical Monthly},
VOLUME = {87},
NUMBER = {5},
YEAR = {1980},
PAGES = {403--404},
DOI = {10.2307/2321223},
NOTE = {MR:1539387.},
ISSN = {0002-9890},
}
G. E. Andrews and R. Askey :
“Another \( q \) -extension of the beta function ,”
Proc. Am. Math. Soc.
81 : 1
(January 1981 ),
pp. 97–100 .
MR
589145
Zbl
0471.33001
article
Abstract
People
BibTeX
@article {key589145m,
AUTHOR = {Andrews, George E. and Askey, Richard},
TITLE = {Another \$q\$-extension of the beta function},
JOURNAL = {Proc. Am. Math. Soc.},
FJOURNAL = {Proceedings of the American Mathematical
Society},
VOLUME = {81},
NUMBER = {1},
MONTH = {January},
YEAR = {1981},
PAGES = {97--100},
DOI = {10.2307/2043995},
NOTE = {MR:589145. Zbl:0471.33001.},
ISSN = {0002-9939},
}
G. E. Andrews and R. Askey :
“Classical orthogonal polynomials ,”
pp. 36–62
in
Polynômes orthogonaux et applications
[Orthogonal polynomials and applications ]
(Bar-le-Duc, France, 15–18 October 1984 ).
Edited by C. Brezinski, A. Draux, A. P. Magnus, P. Maroni, and A. Ronveaux .
Lecture Notes in Mathematics 1171 .
Springer (Berlin ),
1985 .
MR
838970
Zbl
0596.33016
incollection
Abstract
People
BibTeX
There have been a number of definitions of the classical orthogonal polynomials, but each definition has left out some important orthogonal polynomials which have enough nice properties to justify including them in the category of classical orthogonal polynomials. We summarize some of the previous work on classical orthogonal polynomials, state our definition, and give a few new orthogonality relations for some of the classical orthogonal polynomials.
@incollection {key838970m,
AUTHOR = {Andrews, George E. and Askey, Richard},
TITLE = {Classical orthogonal polynomials},
BOOKTITLE = {Polyn\^omes orthogonaux et applications
[Orthogonal polynomials and applications]},
EDITOR = {Brezinski, C. and Draux, A. and Magnus,
A. P. and Maroni, P. and Ronveaux, A.},
SERIES = {Lecture Notes in Mathematics},
NUMBER = {1171},
PUBLISHER = {Springer},
ADDRESS = {Berlin},
YEAR = {1985},
PAGES = {36--62},
DOI = {10.1007/BFb0076530},
NOTE = {(Bar-le-Duc, France, 15--18 October
1984). MR:838970. Zbl:0596.33016.},
ISSN = {0075-8434},
ISBN = {9783540397434},
}
Ramanujan revisited
(Urbana-Champaign, IL, 1–5 June 1987 ).
Edited by G. E. Andrews, R. A. Askey, B. C. Berndt, K. G. Ramanathan, and R. A. Rankin .
Academic Press (Boston ),
1988 .
MR
938955
Zbl
0635.00003
book
People
BibTeX
@book {key938955m,
TITLE = {Ramanujan revisited},
EDITOR = {Andrews, George E. and Askey, Richard
A. and Berndt, Bruce C. and Ramanathan,
K. G. and Rankin, Robert A.},
PUBLISHER = {Academic Press},
ADDRESS = {Boston},
YEAR = {1988},
PAGES = {xx + 609},
NOTE = {(Urbana-Champaign, IL, 1--5 June 1987).
MR:938955. Zbl:0635.00003.},
ISBN = {9780120585601},
}
R. Askey :
“Beta integrals in Ramanujan’s papers, his unpublished work and further examples ,”
pp. 561–590
in
Ramanujan revisited
(Urbana-Champaign, IL, 1–5 June 1987 ).
Edited by G. E. Andrews, R. A. Askey, B. C. Berndt, K. G. Ramanathan, and R. A. Rankin .
Academic Press (Boston ),
1988 .
MR
938979
Zbl
0648.33001
incollection
People
BibTeX
@incollection {key938979m,
AUTHOR = {Askey, Richard},
TITLE = {Beta integrals in {R}amanujan's papers,
his unpublished work and further examples},
BOOKTITLE = {Ramanujan revisited},
EDITOR = {Andrews, George E. and Askey, Richard
A. and Berndt, Bruce C. and Ramanathan,
K. G. and Rankin, Robert A.},
PUBLISHER = {Academic Press},
ADDRESS = {Boston},
YEAR = {1988},
PAGES = {561--590},
NOTE = {(Urbana-Champaign, IL, 1--5 June 1987).
MR:938979. Zbl:0648.33001.},
ISBN = {9780120585601},
}
R. Askey :
“The work of George Andrews: A Madison perspective ”
in
The Andrews Festschrift
(Maratea, Italy, 31 August–6 September 1998 ),
published as Sém. Lothar. Combin.
42 .
Issue edited by D. Foata and G.-N. Han .
Universität Wien ,
1999 .
Article B42b, 24 pages.
MR
1701581
Zbl
1041.01505
incollection
Abstract
People
BibTeX
In his own contribution to this volume, George Andrews has touched on a number of themes in his research by looking at the early influences on him of Bailey, Fine, MacMahon, Rademacher and Ramanujan. In this paper, I propose to present a survey of his work organized on a different theme. George has often alluded to the fact that his 1975–76 year in Madison was extremely important in his work. So it seems a reasonable project to survey his career from a Madison perspective. To make this story complete, I begin with Andrews’ work in the late 1960’s that led inexorably to our eventual lengthy collaboration. The year in Madison set in motion three seemingly separate strands of research that were fundamental in much of his subsequent work. Then I briefly describe his collaboration with Rodney Baxter and the discovery of the crank.
@article {key1701581m,
AUTHOR = {Askey, Richard},
TITLE = {The work of {G}eorge {A}ndrews: {A}
{M}adison perspective},
JOURNAL = {S\'em. Lothar. Combin.},
FJOURNAL = {S\'eminaire Lotharingien de Combinatoire},
VOLUME = {42},
YEAR = {1999},
URL = {https://www.mat.univie.ac.at/~slc/wpapers/s42askey.pdf},
NOTE = {\textit{The {A}ndrews {F}estschrift}
(Maratea, Italy, 31 August--6 September
1998). Issue edited by D. Foata
and G.-N. Han. Article B42b, 24
pages. MR:1701581. Zbl:1041.01505.},
ISSN = {1286-4889},
}
G. E. Andrews, R. Askey, and R. Roy :
Special functions .
Encyclopedia of Mathematics and its Applications 71 .
Cambridge University Press ,
1999 .
A paperback edition was published in 2000 .
MR
1688958
Zbl
0920.33001
book
People
BibTeX
@book {key1688958m,
AUTHOR = {Andrews, George E. and Askey, Richard
and Roy, Ranjan},
TITLE = {Special functions},
SERIES = {Encyclopedia of Mathematics and its
Applications},
NUMBER = {71},
PUBLISHER = {Cambridge University Press},
YEAR = {1999},
PAGES = {xvi+664},
DOI = {10.1017/CBO9781107325937},
NOTE = {A paperback edition was published in
2000. MR:1688958. Zbl:0920.33001.},
ISSN = {0953-4806},
ISBN = {9780521623216},
}
G. E. Andrews, R. Askey, and R. Roy :
Special functions ,
Paperback edition.
Encyclopedia of Mathematics and Its Applications 71 .
Cambridge University Press ,
2000 .
The original hardback edition was published in 1999 .
Zbl
1075.33500
book
People
BibTeX
@book {key1075.33500z,
AUTHOR = {Andrews, George E. and Askey, Richard
and Roy, Ranjan},
TITLE = {Special functions},
EDITION = {Paperback},
SERIES = {Encyclopedia of Mathematics and Its
Applications},
NUMBER = {71},
PUBLISHER = {Cambridge University Press},
YEAR = {2000},
PAGES = {xvi + 664},
NOTE = {The original hardback edition was published
in 1999. Zbl:1075.33500.},
ISSN = {0953-4806},
ISBN = {9780521789882},
}
G. E. Andrews, G. Gasper, and S. Suslov :
“Preface ,”
pp. 5–6
in
Askey special issues ,
published as Ramanujan J.
13 : 1–3 .
Springer (New York ),
June 2007 .
MR
2281153
Zbl
1186.00042
incollection
People
BibTeX
@article {key2281153m,
AUTHOR = {Andrews, George E. and Gasper, George
and Suslov, Sergei},
TITLE = {Preface},
JOURNAL = {Ramanujan J.},
FJOURNAL = {The Ramanujan Journal},
VOLUME = {13},
NUMBER = {1--3},
MONTH = {June},
YEAR = {2007},
PAGES = {5--6},
DOI = {10.1007/s11139-006-0239-z},
NOTE = {\textit{Askey special issues}. MR:2281153.
Zbl:1186.00042.},
ISSN = {1382-4090},
}