Olver%20algorithm

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1: Bibliography S

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Uniform asymptotic forms of modified Mathieu functions. Quart. J. Mech. Appl. Math. 20 (3), pp. 365–380.

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External Links:

Document, MathReview (F. W. J. Olver), ZentralBlatt

Referenced by:

§28.8(iv).

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Algorithm AS 239. Chi-squared and incomplete gamma integral. Appl. Statist. 37 (3), pp. 466–473.

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Notes:

Double-precision Fortran.

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FullText, Code

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5th item.

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Matrix Algorithms. Vol. 2: Eigensystems. Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA.

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External Links:

ISBN 0-89871-503-2, MathReview Entry, ZentralBlatt

Referenced by:

§3.2(vi).

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A stable quotient-difference algorithm. Math. Comp. 34 (150), pp. 515–519.

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External Links:

ISSN 0025-5718, FullText, MathReview, ZentralBlatt

Referenced by:

§3.10(ii).

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Department of Computer Science, Stony Brook University, New York.

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Notes:

A collection of over 70 combinatorial algorithms.

External Links:

Stony Brook Algorithm Repository

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7th item.

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2: Bibliography O

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Note on backward recurrence algorithms. Math. Comp. 26 (120), pp. 941–947.

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External Links:

FullText, MathReview (Walter Gautschi), ZentralBlatt

Referenced by:

§10.74(iv), §3.6(v).

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Error analysis of Miller’s recurrence algorithm. Math. Comp. 18 (85), pp. 65–74.

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External Links:

FullText, MathReview (J.C.P. Miller), ZentralBlatt

Referenced by:

§3.6(iii).

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A paradox in asymptotics. SIAM J. Math. Anal. 1 (4), pp. 533–534.

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External Links:

Document, MathReview (L. Hoischen), ZentralBlatt

Referenced by:

§2.10(iv).

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Error bounds for stationary phase approximations. SIAM J. Math. Anal. 5 (1), pp. 19–29.

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Notes:

See also Olver (1997b)

External Links:

Document, MathReview (L. Berg), ZentralBlatt

Referenced by:

§2.3(iv).

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Second-order differential equations with fractional transition points. Trans. Amer. Math. Soc. 226, pp. 227–241.

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External Links:

FullText, MathReview (Anthony Leung), ZentralBlatt

Referenced by:

§2.8(v).

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3: Bibliography

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Algorithm 724: Program to calculate F-percentiles. ACM Trans. Math. Software 19 (4), pp. 481–483.

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Notes:

Double-precision Fortran, maximum accuracy 13D.

External Links:

ISSN 0098-3500, Document, GAMS (module 724; package TOMS), ZentralBlatt

Referenced by:

1st item.

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Algorithm 39: Areas under the normal curve. The Computer Journal 12 (2), pp. 197–198.

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Notes:

Includes Algol program, maximum accuracy 12D.

External Links:

Document

Referenced by:

§7.25(ii).

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Application of the combined nonlinear-condensation transformation to problems in statistical analysis and theoretical physics. Comput. Phys. Comm. 150 (1), pp. 1–20.

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Notes:

Includes algorithms for Lerch’s transcendent. C and Mathematica codes by Aksenov and Jentschura are available.

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Code, Document

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1st item.

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Algorithms for special integrals of ordinary differential equations. J. Phys. A 29 (5), pp. 973–991.

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ISSN 0305-4470, Document, MathReview, ZentralBlatt

Referenced by:

§32.10(i).

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Algorithm 804: Subroutines for the computation of Mathieu functions of integer orders. ACM Trans. Math. Software 26 (3), pp. 408–414.

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Notes:

Double-precision C++, minimum accuracy 14D

External Links:

ISSN 0098-3500, Document, GAMS (module 804; package TOMS)

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1st item, 1st item.

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4: Bibliography F

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Algorithms and codes for the Macdonald function: Recent progress and comparisons. J. Comput. Appl. Math. 161 (1), pp. 179–192.

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External Links:

ISSN 0377-0427, MathReview (Boro Döring), ZentralBlatt

Referenced by:

§10.77(vi).

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Algorithm 838: Airy functions. ACM Trans. Math. Software 30 (4), pp. 491–501.

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Notes:

Single- and double-precision Fortran, maximum accuracy 32S.

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ISSN 0098-3500, Document, Code, MathReview Entry, ZentralBlatt

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3rd item, 2nd item, 1st item.

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Sur certaines sommes des intégral-cosinus. Bull. Soc. Math. Phys. Serbie 12, pp. 13–20 (French).

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External Links:

MathReview (L. Carlitz), ZentralBlatt

Referenced by:

§6.15.

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Algorithm 309. Gamma function with arbitrary precision. Comm. ACM 10 (8), pp. 511–512.

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External Links:

ISSN 0001-0782, Document

Referenced by:

§5.24(ii).

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Algorithm 435: Modified incomplete gamma function. Comm. ACM 15 (11), pp. 993–995.

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Notes:

Includes Fortran code. For a Remark see ACM Trans. Math. Software 4 (1978), no. 3, pp. 296–304.

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ISSN 0001-0782, Document, Remark

Referenced by:

§8.28(ii).

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5: Bibliography B

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Pionic atoms. Annual Review of Nuclear and Particle Science 20, pp. 467–508.

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External Links:

Document

Referenced by:

§33.22(iv).

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Algorithm 719: Multiprecision translation and execution of Fortran programs. ACM Trans. Math. Software 19 (3), pp. 288–319.

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External Links:

ISSN 0098-3500, Document, GAMS (module 719; package TOMS), C++ wrapper, ZentralBlatt

Referenced by:

3rd item, 2nd item.

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An algorithm for regular and irregular Coulomb and Bessel functions of real order to machine accuracy. Comput. Phys. Comm. 21 (3), pp. 297–314.

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External Links:

Document

Referenced by:

§3.10(iii), §33.22(iv).

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Coulomb functions (negative energies). Comput. Phys. Comm. 20 (3), pp. 447–458.

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Notes:

Double-precision Fortran code.

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Document, Code

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1st item, 4th item.

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Some solutions of the problem of forced convection. Philos. Mag. Series 7 20, pp. 322–343.

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External Links:

Document, ZentralBlatt

Referenced by:

§10.73(iv).

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6: 2.11 Remainder Terms; Stokes Phenomenon

… ►Further details for this example are supplied in Olver (1991a, 1994b). … ►For further details see Olde Daalhuis and Olver (1994). … ►For second-order differential equations, see Olde Daalhuis and Olver (1995a), Olde Daalhuis (1995, 1996), and Murphy and Wood (1997). … ►Similar improvements are achievable by Aitken’s ${\mathrm{\Delta }}^2$-process, Wynn’s $ϵ$-algorithm, and other acceleration transformations. … ►For example, using double precision $d_{20}$ is found to agree with (2.11.31) to 13D. …

7: Bibliography K

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Linear convergence and the bisection algorithm. Amer. Math. Monthly 93 (1), pp. 48–51.

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External Links:

ISSN 0002-9890, FullText, MathReview (J. G. Herriot), ZentralBlatt

Referenced by:

§3.8(iii).

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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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External Links:

ISSN 0098-3500, Document, GAMS (module 737; package TOMS), ZentralBlatt

Referenced by:

1st item.

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Algorithm 763: INTERVAL_ARITHMETIC: A Fortran 90 module for an interval data type. ACM Trans. Math. Software 22 (4), pp. 385–392.

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ISSN 0098-3500, Document, GAMS (module 763; package TOMS), ZentralBlatt

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2nd item.

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Algorithm 327: Dilogarithm [S22]. Comm. ACM 11 (4), pp. 270–271.

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Notes:

Includes Algol program, maximum accuracy 12D.

External Links:

ISSN 0001-0782, Document

Referenced by:

§25.21(v).

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Algorithm 421. Complex gamma function with error control. Comm. ACM 15 (4), pp. 271–272.

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External Links:

ISSN 0001-0782, Document

Referenced by:

§5.24(iv).

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8: Bibliography L

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Algorithm 917: complex double-precision evaluation of the Wright $\omega$ function. ACM Trans. Math. Software 38 (3), pp. Art. 20, 17.

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External Links:

ISSN 0098-3500, Document, FullText, MathReview Entry, ZentralBlatt

Referenced by:

§4.13, 2nd item, §4.48(iv).

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An asymptotic estimate for the Bernoulli and Euler numbers. Canad. Math. Bull. 20 (1), pp. 109–111.

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External Links:

MathReview (D. H. Lehmer), ZentralBlatt

Referenced by:

§24.11.

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Algorithm 244: Fresnel integrals. Comm. ACM 7 (11), pp. 660–661.

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Notes:

Includes Algol program, maximum accuracy 12D.

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ISSN 0001-0782, Document

Referenced by:

§7.25(iv).

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Algorithms for rational approximations for a confluent hypergeometric function. Utilitas Math. 11, pp. 123–151.

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External Links:

MathReview (F. Gotze), ZentralBlatt

Referenced by:

§13.31(iii).

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Algorithms for the Computation of Mathematical Functions. Academic Press, New York.

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External Links:

MathReview (Gh. Adam)

Referenced by:

§16.26.

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9: Bibliography C

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Combinatorics: Topics, Techniques, Algorithms. Cambridge University Press, Cambridge.

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ISBN 0-521-45133-7; 0-521-45761-0, MathReview (E. J. F. Primrose), ZentralBlatt

Referenced by:

§26.13.

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An algorithm for the Fourier-Bessel transform. Comput. Phys. Comm. 23 (4), pp. 343–353.

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ISSN 0010-4655, Document, MathReview

Referenced by:

§10.74(vii).

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Algorithm 577: Algorithm for incomplete elliptic intergrals [S21]. ACM Trans. Math. Software 7 (3), pp. 398–403.

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External Links:

ISSN 0098-3500, Document, GAMS (module 577; package TOMS), ZentralBlatt

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1st item.

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An algorithm for computing logarithms and arctangents. Math. Comp. 26 (118), pp. 543–549.

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External Links:

FullText, MathReview (F. Gotze), ZentralBlatt

Referenced by:

§4.45(i).

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Algorithms for Modular Elliptic Curves. 2nd edition, Cambridge University Press, Cambridge.

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External Links:

ISBN 0-521-59820-6, MathReview (Joseph H. Silverman), ZentralBlatt

Referenced by:

§23.20(ii).

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10: Bibliography W

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The Nahm equations, finite-gap potentials and Lamé functions. J. Phys. A 20 (10), pp. 2679–2683.

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ISSN 0305-4470, Document, MathReview (James M. D’Archangelo), ZentralBlatt

Referenced by:

§29.19(ii).

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Algorithm 794: Numerical Hankel transform by the Fortran program HANKEL. ACM Trans. Math. Software 25 (2), pp. 240–250.

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Notes:

Double-precision Fortran, maximum accuracy 10S.

External Links:

ISSN 0098-3500, Document, GAMS (module 794; package TOMS), ZentralBlatt

Referenced by:

7th item, 10th item.

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A rational approximant for the digamma function. Numer. Algorithms 33 (1-4), pp. 499–507.

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Notes:

International Conference on Numerical Algorithms, Vol. I (Marrakesh, 2001)

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ISSN 1017-1398, Document, MathReview, ZentralBlatt

Referenced by:

§3.9(vi), §5.23(i).

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An algorithmic proof theory for hypergeometric (ordinary and “$q$”) multisum/integral identities. Invent. Math. 108, pp. 575–633.

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ISSN 0020-9910, Document, MathReview (David R. Masson), ZentralBlatt

Referenced by:

§16.4(iii).

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Algorithm 44: Bessel functions computed recursively. Comm. ACM 4 (4), pp. 177–178.

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Notes:

Includes Algol code, maximum accuracy 8S.

External Links:

ISSN 0001-0782, Document

Referenced by:

§10.77(ii).

Encodings:

BibTeX

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