Padé approximations

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11: 33.23 Methods of Computation

… ►Thompson and Barnett (1985, 1986) and Thompson (2004) use combinations of series, continued fractions, and Padé-accelerated asymptotic expansions (§3.11(iv)) for the analytic continuations of Coulomb functions. … ►

§33.23(vii) WKBJ Approximations

►WKBJ approximations (§2.7(iii)) for $\rho >{\rho }_{\mathrm{tp}}(\eta ,\mathrm{\ell })$ are presented in Hull and Breit (1959) and Seaton and Peach (1962: in Eq. …Seaton (1984) estimates the accuracies of these approximations. ►Hull and Breit (1959) and Barnett (1981b) give WKBJ approximations for $F_0$ and $G_0$ in the region inside the turning point: .

12: Bibliography W

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Asymptotic approximations for certain $6$-$j$ and $9$-$j$ symbols. J. Phys. A 32 (39), pp. 6901–6902.

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ISSN 0305-4470, Document, MathReview, ZentralBlatt

Referenced by:

§34.8, §34.8.

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Rational approximations for the modified Bessel function of the second kind. Comput. Phys. Comm. 59 (3), pp. 471–493.

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ISSN 0010-4655, Document, MathReview, ZentralBlatt

Referenced by:

§10.76(ii).

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Asymptotic Approximations to Truncation Errors of Series Representations for Special Functions. In Algorithms for Approximation, A. Iske and J. Levesley (Eds.), pp. 331–348.

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ISBN 3-540-33283-9, Document, MathReview Entry, ZentralBlatt

Referenced by:

§2.10(i).

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Some explicit Padé approximants for the function ${\mathrm{\Phi }}^{\prime }/\mathrm{\Phi }$ and a related quadrature formula involving Bessel functions. SIAM J. Math. Anal. 16 (4), pp. 887–895.

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ISSN 0036-1410, Document, MathReview (Wyman Fair), ZentralBlatt

Referenced by:

§13.31(ii).

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Upon systems of recursions which obtain among the quotients of the Padé table. Numer. Math. 8 (3), pp. 264–269.

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ISSN 0029-599X, Document, MathReview (F. L. Bauer), ZentralBlatt

Referenced by:

§3.11(iv).

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13: Bibliography

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Efficient approximation of the Struve functions ${𝐇}_n$ occurring in the calculation of sound radiation quantities. The Journal of the Acoustical Society of America 140 (6), pp. 4154–4160.

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Document

Referenced by:

§11.13(i), §11.13(i).

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Shanks’ convergence acceleration transform, Padé approximants and partitions. J. Combin. Theory Ser. A 43 (1), pp. 70–84.

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ISSN 0097-3165, Document, MathReview (Kenneth A. Jukes), ZentralBlatt

Referenced by:

§17.18.

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Rational function approximations for Fermi-Dirac integrals. The Astrophysical Journal Supplement Series 84, pp. 101–108.

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Notes:

Double-precision Fortran, maximum precision 8D.

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ISSN 0067-0049, Document, Code

Referenced by:

5th item, 1st item.

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