interrelations%20with%20other%20orthogonal%20polynomials
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21: 3.8 Nonlinear Equations
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§3.8(iii) Other Methods
… ►For other efficient derivative-free methods, see Le (1985). … ►Consider and . We have and . … ►Corresponding numerical factors in this example for other zeros and other values of are obtained in Gautschi (1984, §4). …22: 24.1 Special Notation
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►(For other notation see Notation for the Special Functions.)
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Bernoulli Numbers and Polynomials
►The origin of the notation , , is not clear. … ►Euler Numbers and Polynomials
… ►Other historical remarks on notations can be found in Cajori (1929, pp. 42–44). …23: 13.30 Tables
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►For other tables prior to 1961 see Fletcher et al. (1962) and Lebedev and Fedorova (1960).
Zhang and Jin (1996, pp. 411–423) tabulates and for , , and , 8S (for ) and 7S (for ).
24: 10.75 Tables
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Achenbach (1986) tabulates , , , , , 20D or 18–20S.
Bickley et al. (1952) tabulates or , or , , (.01 or .1) 10(.1) 20, 8S; , , , or , 10S.
Kerimov and Skorokhodov (1984b) tabulates all zeros of the principal values of and , for , 9S.
Zhang and Jin (1996, p. 322) tabulates , , , , , , , , , 7S.
Zhang and Jin (1996, p. 323) tabulates the first real zeros of , , , , , , , , 8D.
25: 18.3 Definitions
§18.3 Definitions
… ►As given by a Rodrigues formula (18.5.5).
Jacobi on Other Intervals
…26: 31.16 Mathematical Applications
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§31.16(ii) Heun Polynomial Products
►Expansions of Heun polynomial products in terms of Jacobi polynomial (§18.3) products are derived in Kalnins and Miller (1991a, b, 1993) from the viewpoint of interrelation between two bases in a Hilbert space: ►
31.16.1
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31.16.3
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27: 27.15 Chinese Remainder Theorem
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►Their product has 20 digits, twice the number of digits in the data.
…These numbers, in turn, are combined by the Chinese remainder theorem to obtain the final result , which is correct to 20 digits.
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28: 25.12 Polylogarithms
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►Other notations and names for include (Kölbig et al. (1970)), Spence function (’t Hooft and Veltman (1979)), and (Maximon (2003)).
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►For other values of , is defined by analytic continuation.
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►Further properties include
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►In terms of polylogarithms
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29: Bibliography K
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Algorithm 737: INTLIB: A portable Fortran 77 interval standard-function library.
ACM Trans. Math. Software 20 (4), pp. 447–459.
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Methods of computing the Riemann zeta-function and some generalizations of it.
USSR Comput. Math. and Math. Phys. 20 (6), pp. 212–230.
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Connection formulae for asymptotics of solutions of the degenerate third Painlevé equation. I.
Inverse Problems 20 (4), pp. 1165–1206.
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The Askey scheme as a four-manifold with corners.
Ramanujan J. 20 (3), pp. 409–439.
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HYP and HYPQ. Mathematica packages for the manipulation of binomial sums and hypergeometric series respectively -binomial sums and basic hypergeometric series.
Séminaire Lotharingien de Combinatoire 30, pp. 61–76.
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