representation as sums of powers
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21—26 of 26 matching pages
21: Bibliography R
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A non-negative representation of the linearization coefficients of the product of Jacobi polynomials.
Canad. J. Math. 33 (4), pp. 915–928.
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Integral representations for products of Airy functions.
Z. Angew. Math. Phys. 46 (2), pp. 159–170.
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Integral representations for products of Airy functions. II. Cubic products.
Z. Angew. Math. Phys. 48 (4), pp. 646–655.
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Integral representations for products of Airy functions. III. Quartic products.
Z. Angew. Math. Phys. 48 (4), pp. 656–664.
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Research Institute for Symbolic Computation, Hagenberg im Mühlkreis, Austria.
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22: 32.8 Rational Solutions
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►where the are monic polynomials (coefficient of highest power of is ) satisfying
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32.8.8
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►For determinantal representations see Kajiwara and Masuda (1999).
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►For determinantal representations see Kajiwara and Ohta (1998) and Noumi and Yamada (1999).
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►For determinantal representations see Masuda et al. (2002).
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23: Errata
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►For some classical polynomials we give some positive sums and discriminants.
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Section 16.11(i)
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Additions
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Equation (11.11.1)
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Subsections 2.3(ii), 2.3(iv), 2.3(vi)
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Pochhammer symbol representations for the functions and were inserted.
Clarifications regarding -powers and asymptotics were added, along with extra citations.
24: 11.10 Anger–Weber Functions
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§11.10(i) Definitions
… ►§11.10(iii) Maclaurin Series
… ►§11.10(x) Integrals and Sums
►For collections of integral representations and integrals see Erdélyi et al. (1954a, §§4.19 and 5.17), Marichev (1983, pp. 194–195 and 214–215), Oberhettinger (1972, p. 128), Oberhettinger (1974, §§1.12 and 2.7), Oberhettinger (1990, pp. 105 and 189–190), Prudnikov et al. (1990, §§1.5 and 2.8), Prudnikov et al. (1992a, §3.18), Prudnikov et al. (1992b, §3.18), and Zanovello (1977). ►For sums see Hansen (1975, pp. 456–457) and Prudnikov et al. (1990, §§6.4.2–6.4.3).25: 16.8 Differential Equations
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16.8.4
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16.8.5
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►For other values of the , series solutions in powers of (possibly involving also ) can be constructed via a limiting process; compare §2.7(i) in the case of second-order differential equations.
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16.8.9
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►In this reference it is also explained that in general when no simple representations in terms of generalized hypergeometric functions are available for the fundamental solutions near .
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