q-binomial%20series
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1: 17.5 Functions
2: 26.9 Integer Partitions: Restricted Number and Part Size
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βΊ
26.9.4
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βΊis the Gaussian polynomial (or -binomial coefficient); see also §§17.2(i)–17.2(ii).
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βΊ
26.9.5
βΊ
26.9.6
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βΊ
26.9.7
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3: 17.2 Calculus
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βΊ
§17.2(ii) Binomial Coefficients
βΊ
17.2.27
βΊ
17.2.28
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βΊ
§17.2(iii) Binomial Theorem
… βΊWhen , where is a nonnegative integer, (17.2.37) reduces to the -binomial series …4: 26.10 Integer Partitions: Other Restrictions
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βΊ
Table 26.10.1: Partitions restricted by difference conditions, or equivalently with parts from .
βΊ
βΊ
βΊ
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βΊ
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26.10.3
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5: Bibliography K
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βΊ
Algorithm 737: INTLIB: A portable Fortran 77 interval standard-function library.
ACM Trans. Math. Software 20 (4), pp. 447–459.
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βΊ
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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βΊ
Connection formulae for asymptotics of solutions of the degenerate third Painlevé equation. I.
Inverse Problems 20 (4), pp. 1165–1206.
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βΊ
The Askey scheme as a four-manifold with corners.
Ramanujan J. 20 (3), pp. 409–439.
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βΊ
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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6: 17.3 -Elementary and -Special Functions
7: 26.16 Multiset Permutations
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βΊ
26.16.1
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8: 18.27 -Hahn Class
9: 6.20 Approximations
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βΊ
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βΊ
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βΊ
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βΊ
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Cody and Thacher (1968) provides minimax rational approximations for , with accuracies up to 20S.
Cody and Thacher (1969) provides minimax rational approximations for , with accuracies up to 20S.
MacLeod (1996b) provides rational approximations for the sine and cosine integrals and for the auxiliary functions and , with accuracies up to 20S.
§6.20(ii) Expansions in Chebyshev Series
… βΊLuke and Wimp (1963) covers for (20D), and and for (20D).
10: 25.20 Approximations
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βΊ
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βΊ
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βΊ
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βΊ
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Cody et al. (1971) gives rational approximations for in the form of quotients of polynomials or quotients of Chebyshev series. The ranges covered are , , , . Precision is varied, with a maximum of 20S.
Piessens and Branders (1972) gives the coefficients of the Chebyshev-series expansions of and , , for (23D).