double argument

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1: 22.6 Elementary Identities

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§22.6(ii) Double Argument

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2: Bibliography T

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COULCC: A continued-fraction algorithm for Coulomb functions of complex order with complex arguments. Comput. Phys. Comm. 36 (4), pp. 363–372.

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Notes:

Double-precision Fortran, minimum accuracy: 14D. See also Thompson (2004)

External Links:

Document, Code, ZentralBlatt

Referenced by:

1st item, §33.23(vi), 3rd item.

Encodings:

BibTeX

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Modified Bessel functions $I_{\nu }(z)$ and $K_{\nu }(z)$ of real order and complex argument, to selected accuracy. Comput. Phys. Comm. 47 (2-3), pp. 245–257.

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Notes:

For erratum see same journal 159 (2004), no. 3, p. 243. Double-precision Fortran, accuracy 24S, but can be increased.

External Links:

ISSN 0010-4655, Document, Code, MathReview (John P. Coleman)

Referenced by:

3rd item, 4th item.

Encodings:

BibTeX

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3: Bibliography B

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A program for computing the Riemann zeta function for complex argument. Comput. Phys. Comm. 20 (3), pp. 441–445.

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Notes:

Double-precision Fortran, maximum accuracy 10S.

External Links:

Document, Code, ZentralBlatt

Referenced by:

1st item.

Encodings:

BibTeX

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COULFG: Coulomb and Bessel functions and their derivatives, for real arguments, by Steed’s method. Comput. Phys. Comm. 27, pp. 147–166.

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Notes:

Double-precision Fortran code for positive energies. Maximum accuracy: 31S.

External Links:

Document, Code

Referenced by:

2nd item, 2nd item.

Encodings:

BibTeX

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Algorithm 484: Evaluation of the modified Bessel functions K0(Z) and K1(Z) for complex arguments. Comm. ACM 17 (9), pp. 524–526.

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Notes:

Double-precision Fortran code, maximum accuracy 13S.

External Links:

ISSN 0001-0782, Document, Code

Referenced by:

1st item.

Encodings:

BibTeX

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4: Bibliography G

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Evaluation of Legendre functions of argument greater than one. Comput. Phys. Comm. 105 (2-3), pp. 273–283.

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Notes:

Double-precision Fortran, maximum accuracy 18S

External Links:

ISSN 0010-4655, Document, Code, MathReview, ZentralBlatt

Referenced by:

4th item.

Encodings:

BibTeX

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Algorithm 490: The Dilogarithm function of a real argument [S22]. Comm. ACM 18 (4), pp. 200–202.

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Notes:

Double-precision Fortran, minimum accuracy 15D. For remark see ACM Trans. Math. Software 2 (1976), p. 112

External Links:

ISSN 0001-0782, Document, Code

Referenced by:

2nd item.

Encodings:

BibTeX

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5: Bibliography C

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Bessel functions $J_{\nu }(x)$ and $Y_{\nu }(x)$ of real order and real argument. Comput. Phys. Comm. 18 (1), pp. 133–142.

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Notes:

Double-precision Fortran, maximum accuracy 16S.

External Links:

ISSN 0010-4655, Document, Code

Referenced by:

4th item.

Encodings:

BibTeX

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Bessel functions $I_{\nu }(x)$ and $K_{\nu }(x)$ of real order and complex argument. Comput. Phys. Comm. 24 (1), pp. 97–105.

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Notes:

Double-precision Fortran, maximum accuracy 16S. For erratum see same journal 25 (1982), p. 207.

External Links:

ISSN 0010-4655, Document, Code

Referenced by:

2nd item.

Encodings:

BibTeX

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6: 35.10 Methods of Computation

§35.10 Methods of Computation

… ►Other methods include numerical quadrature applied to double and multiple integral representations. See Yan (1992) for the ${}_1{}^{}F_1^{}$ and ${}_2{}^{}F_1^{}$ functions of matrix argument in the case $m=2$, and Bingham et al. (1992) for Monte Carlo simulation on $𝐎(m)$ applied to a generalization of the integral (35.5.8). …

7: Bibliography D

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Bessel functions $J_n(z)$ and $Y_n(z)$ of integer order and complex argument. Comput. Phys. Comm. 78 (1-2), pp. 181–189.

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Notes:

Double-precision Pascal, maximum accuracy 7D.

External Links:

ISSN 0010-4655, Document, Code, MathReview (J. P. Singhal), ZentralBlatt

Referenced by:

2nd item.

Encodings:

BibTeX

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8: Bibliography K

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ZEBEC: A mathematical software package for computing simple zeros of Bessel functions of real order and complex argument. Comput. Phys. Comm. 113 (2-3), pp. 220–238.

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Notes:

Double-precision Fortran, maximum accuracy 25S.

External Links:

ISSN 0010-4655, Document, Code, ZentralBlatt

Referenced by:

2nd item.

Encodings:

BibTeX

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9: Bibliography

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Algorithm 644: A portable package for Bessel functions of a complex argument and nonnegative order. ACM Trans. Math. Software 12 (3), pp. 265–273.

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Notes:

Single and double precision, maximum accuracy 18S.

External Links:

ISSN 0098-3500, Document, Remark #1. Remark #2. GAMS (module 644; package TOMS), MathReview Entry, ZentralBlatt

Referenced by:

1st item, 1st item, 2nd item, 1st item.

Encodings:

BibTeX

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Algorithm 683: A portable FORTRAN subroutine for exponential integrals of a complex argument. ACM Trans. Math. Software 16 (2), pp. 178–182.

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Notes:

Double- and single-precision Fortran, maximum accuracy 18S or 14S.

External Links:

ISSN 0098-3500, Document, GAMS (module 683; package TOMS), MathReview, ZentralBlatt

Referenced by:

1st item, 1st item.

Encodings:

BibTeX

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10: Bibliography N

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Algorithm 707: CONHYP: A numerical evaluator of the confluent hypergeometric function for complex arguments of large magnitudes. ACM Trans. Math. Software 18 (3), pp. 345–349.

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Notes:

Double-precision Fortran, minimum accuracy 9S, maximum accuracy 13S.

External Links:

ISSN 0098-3500, Document, GAMS (module 707; package TOMS), ZentralBlatt

Referenced by:

1st item.

Encodings:

BibTeX

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