Special functions
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Societies and conference series
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Handbooks
- Bateman project
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Digital Library of Mathematical Functions (DLMF)
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Askey scheme
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Some basic hypergeometric
orthogonal polynomials that generalize Jacobi polynomials by
R. Askey and J. Wilson, Mem. Amer. Math. Soc. 54 (1985), no. 319.
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Hypergeometric orthogonal polynomials and their q-analogues
by Roelof Koekoek,
Peter A. Lesky and René Swarttouw;
Springer-Verlag, 2010.
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Chapters 9 (Hypergeometric orthogonal polynomials) and 14
(Basic hypergeometric polynomials) of the above
book are a slightly extended and updated version of
The Askey-scheme
of hypergeometric orthogonal polynomials and its q-analogue
by
R. Koekoek & R.F. Swarttouw,
Report no. 98-17, 1998, Delft Technical University.
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Online version of the above report
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Askey scheme and q-Askey scheme charts in various formats
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Askey scheme with pictures (jpg file)
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The origin of the Askey scheme:
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Michael Hoare's seven-fold way of
orthogonal polynomials and
seven-fold way of
probability distributions as presented by him at an
Oberwalfach meeting in 1977 on Combinatorics and Special Functions.
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Dick Askey's account
of Michael Hoare's presentation and its aftermath
(in pp. v and vi of Tom Koornwinder's Foreword to the book
Hypergeometric orthogonal polynomials and their q-analogues
by R. Koekoek, P.A. Lesky and R.F. Swarttouw, Springer-Verlag, 2010.
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J. Labelle,
Tableau d'Askey,
in: Orthogonal polynomials and applications (Bar-le-Duc, 1984),
Lecture Notes in Math. 1171, pp. xxxvi--xxxvii, Springer-Verlag, 1985
(Labelle's poster with short introduction).
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J. Labelle,
Askey's
scheme of hypergeometric orthogonal polynomials, 1990
(Labelle's poster, with details spread over a number of pages).
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Josef Meixner:
His life and his orthogonal polynomials, paper by Paul Butzer
and Tom Koornwinder, Indag. Math. (N.S.) 30 (2019), 250-264;
arXiv:1609.02588v3 [math.HO].
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Historical page in Ukrainian about Krawtchouk
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Gradshteyn and Ryzhik,
Table of Integrals, Series, and Products
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Handbook of Continued Fractions for Special Functions
(A.A.M. Cuyt, V. Petersen,
B. Verdonk, H. Waadeland, W.B. Jones)
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Macdonald theory
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A new
class of symmetric functions by I.G. Macdonald,
Séminaire Lotharingien de Combinatoire, B20a (1988), 41 pp.
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Symmetric functions and Hall polynomials
by I.G. Macdonald, Oxford University Press,
Second ed., 1995.
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Orthogonal polynomials associated with root systems
by I.G. Macdonald,
Séminaire Lotharingien Combinatoire 45 (2000), B45a, 40 pp.
(from his 1987 manuscript)
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Affine
Hecke algebras and orthogonal polynomials by I.G. Macdonald,
Séminaire Bourbaki 37 (1994-1995), exp. no. 797 (1995), 189-207.
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Affine Hecke algebras
and orthogonal polynomials by I.G. Macdonald,
Cambridge University Press, 2003.
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Hypergeometric functions I
and Hypergeometric functions II
(q-analogues) by I.G. Macdonald,
arXiv:1309.4568 and arXiv:1309.5208 (from his manuscripts in 1987 or 1988)
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I.G. Macdonald's honorary doctorate at UvA, January 2002.
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Macdonald polynomials web page (by Mike Zabrocki)
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The
symmetric functions catalog (by
Per Alexandersson).
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Generalized Kostka polynomials:
2005 workshop at AIM
and
introductory webpage
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Dick Askey
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Bibliographies
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Wolfram
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Further online tools
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Frozen projects
to Tom Koornwinder's home page