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11—20 of 610 matching pages
11: 10.31 Power Series
12: Bibliography K
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A proof of Askey’s conjectured -analogue of Selberg’s integral and a conjecture of Morris.
SIAM J. Math. Anal. 19 (4), pp. 969–986.
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A proof of the -Macdonald-Morris conjecture for
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Mem. Amer. Math. Soc. 108 (516), pp. vi+80.
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Two notes on notation.
Amer. Math. Monthly 99 (5), pp. 403–422.
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Nielsen’s generalized polylogarithms.
SIAM J. Math. Anal. 17 (5), pp. 1232–1258.
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Tom Koornwinder’s Personal Collection of Maple Procedures
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13: Bibliography H
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The Laplace transform for expressions that contain a probability function.
Bul. Akad. Štiince RSS Moldoven. 1973 (2), pp. 78–80, 93 (Russian).
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Expansions for the probability function in series of Čebyšev polynomials and Bessel functions.
Bul. Akad. Štiince RSS Moldoven. 1976 (1), pp. 77–80, 96 (Russian).
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Integrals that contain a probability function of complicated arguments.
Bul. Akad. Štiince RSS Moldoven. 1976 (1), pp. 80–84, 96 (Russian).
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Sums with cylindrical functions that reduce to the probability function and to related functions.
Bul. Akad. Shtiintse RSS Moldoven. 1978 (3), pp. 80–84, 95 (Russian).
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Some properties and applications of the repeated integrals of the error function.
Proc. Manchester Lit. Philos. Soc. 80, pp. 85–102.
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14: Bibliography L
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Elliptic Functions and Applications.
Applied Mathematical Sciences, Vol. 80, Springer-Verlag, New York.
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Ramanujan’s function
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Duke Math. J. 10 (3), pp. 483–492.
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Optimal cylindrical and spherical Bessel transforms satisfying bound state boundary conditions.
Comput. Phys. Comm. 99 (2-3), pp. 297–306.
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Recurrence relations for hypergeometric functions of unit argument.
Math. Comp. 45 (172), pp. 521–535.
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Microwave specific attenuation by oblate spheroidal raindrops: An exact analysis of TCS’s in terms of spheroidal wave functions.
J. Electromagn. Waves Appl. 12 (6), pp. 709–711.
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15: 26.13 Permutations: Cycle Notation
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denotes the set of permutations of .
is a one-to-one and onto mapping from to itself.
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►The number of elements of with cycle type is given by (26.4.7).
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►The derangement number, , is the number of elements of with no fixed points:
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►Given a permutation , the inversion number of , denoted , is the least number of adjacent transpositions required to represent .
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16: Bibliography J
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Bounds on Dawson’s integral occurring in the analysis of a line distribution network for electric vehicles.
Eurandom Preprint Series
Technical Report 14, Eurandom, Eindhoven, The Netherlands.
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Density matrix of an impenetrable Bose gas and the fifth Painlevé transcendent.
Phys. D 1 (1), pp. 80–158.
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Differential equations and mathematical biology.
Chapman & Hall/CRC Mathematical Biology and Medicine Series, Chapman & Hall/CRC, Boca Raton, FL.
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Asymptotic behavior of integrals.
SIAM Rev. 14 (2), pp. 286–317.
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Modifications of Coulombic interactions by polarizable atoms.
Math. Proc. Cambridge Philos. Soc. 80 (3), pp. 535–539.
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17: 19.37 Tables
§19.37 Tables
… ►§19.37(ii) Legendre’s Complete Integrals
… ►§19.37(iii) Legendre’s Incomplete Integrals
… ►Tabulated for , , to 10D by Fettis and Caslin (1964) (and warns of inaccuracies in Selfridge and Maxfield (1958) and Paxton and Rollin (1959)). … ► …18: 27.2 Functions
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►Euclid’s Elements (Euclid (1908, Book IX, Proposition 20)) gives an elegant proof that there are infinitely many primes.
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►This is the number of positive integers that are relatively prime to ; is Euler’s totient.
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►This is Jordan’s function.
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►This is Liouville’s function.
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►This is Mangoldt’s function.
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19: 8.23 Statistical Applications
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►In queueing theory the Erlang loss function is used, which can be expressed in terms of the reciprocal of ; see Jagerman (1974) and Cooper (1981, pp. 80, 316–319).
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