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11—20 of 810 matching pages
11: Bibliography B
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Products of generalized hypergeometric series.
Proc. London Math. Soc. (2) 28 (2), pp. 242–254.
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Transformations of generalized hypergeometric series.
Proc. London Math. Soc. (2) 29 (2), pp. 495–502.
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Polynomials defined by a difference system.
J. Math. Anal. Appl. 2 (2), pp. 223–263.
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Quasinormal ringing of Kerr black holes: The excitation factors.
Phys. Rev. D 74 (104020), pp. 1–27.
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Über Sturm-Liouvillesche Polynomsysteme.
Math. Z. 29 (1), pp. 730–736.
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12: 4.17 Special Values and Limits
13: 26.4 Lattice Paths: Multinomial Coefficients and Set Partitions
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►For
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is the number of permutations of with cycles of length 1, cycles of length 2, , and cycles of length :
… is the number of set partitions of with subsets of size 1, subsets of size 2, , and subsets of size :
…For each all possible values of are covered.
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►where the summation is over all nonnegative integers such that .
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14: 28.15 Expansions for Small
15: Staff
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Hans Volkmer, University of Wisconsin, Milwaukee, Chaps. 29, 30
Roderick S. C. Wong, City University of Hong Kong, Chaps. 1, 2, 18
Hans Volkmer, University of Wisconsin–Milwaukee, for Chaps. 29, 30
Roderick S. C. Wong, City University of Hong Kong, for Chaps. 2, 18
16: Publications
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D. W. Lozier, B. R. Miller and B. V. Saunders (1999)
Design of a Digital Mathematical Library for Science, Technology and Education,
Proceedings of the
IEEE Forum on Research and Technology Advances in Digital Libraries (IEEE ADL ’99,
Baltimore, Maryland, May 19, 1999).
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Q. Wang and B. V. Saunders (2005)
Web-Based 3D Visualization in a Digital Library of Mathematical Functions,
Proceedings of the Web3D Symposium,
Bangor, UK, March 29–April 1, 2005.
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B. V. Saunders and Q. Wang (2006)
From B-Spline Mesh Generation to Effective Visualizations for the
NIST Digital Library of Mathematical Functions,
in Curve and Surface Design, Proceedings of the Sixth International
Conference on Curves and Surfaces,
Avignon, France June 29–July 5, 2006,
pp. 235–243.
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B. I. Schneider, B. R. Miller and B. V. Saunders (2018)
NIST’s Digital Library of Mathematial Functions,
Physics Today
71, 2, 48 (2018), pp. 48–53.
17: 26.2 Basic Definitions
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►Thus is the permutation , , .
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►Here , and .
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►A lattice path is a directed path on the plane integer lattice .
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►As an example, , , is a partition of .
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►As an example, is a partition of 13.
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18: 28.6 Expansions for Small
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►For more details on these expansions and recurrence relations for the coefficients see Frenkel and Portugal (2001, §2).
►The coefficients of the power series of , and also , are the same until the terms in and , respectively.
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►Here for , for , and for and .
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►where is the unique root of the equation in the interval , and .
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►For more details on these expansions and recurrence relations for the coefficients see Frenkel and Portugal (2001, §2).
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19: 6.14 Integrals
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6.14.2
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6.14.4
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6.14.6
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6.14.7
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►For collections of integrals, see Apelblat (1983, pp. 110–123), Bierens de Haan (1939, pp. 373–374, 409, 479, 571–572, 637, 664–673, 680–682, 685–697), Erdélyi et al. (1954a, vol. 1, pp. 40–42, 96–98, 177–178, 325), Geller and Ng (1969), Gradshteyn and Ryzhik (2000, §§5.2–5.3 and 6.2–6.27), Marichev (1983, pp. 182–184), Nielsen (1906b), Oberhettinger (1974, pp. 139–141), Oberhettinger (1990, pp. 53–55 and 158–160), Oberhettinger and Badii (1973, pp. 172–179), Prudnikov et al. (1986b, vol. 2, pp. 24–29 and 64–92), Prudnikov et al. (1992a, §§3.4–3.6), Prudnikov et al. (1992b, §§3.4–3.6), and Watrasiewicz (1967).