Coulomb functions

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31: Bibliography T

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Coulomb functions with complex angular momenta. Comput. Phys. Comm. 17 (4), pp. 351–355.

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Notes:

Single-precision Fortran code.

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ISSN 0010-4655, Document, Code

Referenced by:

3rd item, 2nd item.

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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)

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Document, Code, ZentralBlatt

Referenced by:

1st item, §33.23(vi), 3rd item.

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Coulomb and Bessel functions of complex arguments and order. J. Comput. Phys. 64 (2), pp. 490–509.

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ISSN 0021-9991, Document, MathReview (R. C. Varma), ZentralBlatt

Referenced by:

§10.74(v), §13.32(iii), §3.10(iii), §3.10(iii), §33.13, §33.23(vi), §33.26(iii), Ch.33, Erratum (V1.0.24) for Paragraph Steed’s Algorithm (in §3.10(iii)).

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Erratum to “COULCC: A continued-fraction algorithm for Coulomb functions of complex order with complex arguments”. Comput. Phys. Comm. 159 (3), pp. 241–242.

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Document, Code, ZentralBlatt

Referenced by:

§33.23(vi), I. J. Thompson and A. R. Barnett (1985).

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32: Bibliography N

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Coulomb Functions for Large Values of the Parameter $\eta$ . Technical report Atomic Energy of Canada Limited, Chalk River, Ontario.

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Notes:

Rep. CRT-526

External Links:

MathReview (A. Erdélyi)

Referenced by:

§33.7.

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COULN, a program for evaluating negative energy Coulomb functions. Comput. Phys. Comm. 33 (4), pp. 413–419.

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Notes:

Double-precision Fortran code.

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2nd item, 7th item.

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Evaluation of negative energy Coulomb (Whittaker) functions. Comput. Phys. Comm. 159 (1), pp. 55–62.

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Notes:

Double-precision Fortran-90 code.

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Referenced by:

§33.23(vi), 8th item.

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33: 13.18 Relations to Other Functions

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§13.18(vi) Coulomb Functions

►For representations of Coulomb functions in terms of Whittaker functions see (33.2.3), (33.2.7), (33.14.4) and (33.14.7)

34: Bibliography B

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KLEIN: Coulomb functions for real $\lambda$ and positive energy to high accuracy. Comput. Phys. Comm. 24 (2), pp. 141–159.

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Notes:

Double-precision Fortran code for positive energies.

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Referenced by:

5th item, §33.23(vii), 1st item.

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The Calculation of Spherical Bessel Functions and Coulomb Functions. In Computational Atomic Physics: Electron and Positron Collisions with Atoms and Ions, K. Bartschat and J. Hinze (Eds.), pp. 181–202.

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Notes:

Includes program disk. Double-precision Fortran code for positive energies. Maximum accuracy: 15D.

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ISBN 3-540-60179-1, FullText and Code

Referenced by:

3rd item, §33.8.

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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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1st item, 4th item.

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Coulomb functions for large charges and small velocities. Phys. Rev. (2) 97 (2), pp. 542–554.

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External Links:

Document, MathReview (A. Erdélyi), ZentralBlatt

Referenced by:

§33.5(iv).

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Methods of calculation of radial wave functions and new tables of Coulomb functions. Physical Rev. (2) 80, pp. 553–560.

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External Links:

Document, MathReview (S. C. van Veen), ZentralBlatt

Referenced by:

§33.7.

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35: 1.17 Integral and Series Representations of the Dirac Delta

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Coulomb Functions (§33.14(iv))

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1.17.15 $$\delta \left(x-a\right)={\int }_0^{\mathrm{\infty }}s(x,\mathrm{\ell };r)s(a,\mathrm{\ell };r)dr,$$ $a>0$, $x>0$.

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Symbols:

$s(ϵ,\mathrm{\ell };r)$: regular Coulomb function, $\delta \left(x-a\right)$: Dirac delta (or Dirac delta function), $dx$: differential of $x$ and $\int$: integral

Permalink:

http://dlmf.nist.gov/1.17.E15

Encodings:

pMML, png, TeX

See also:

Annotations for §1.17(ii), §1.17(ii), §1.17 and Ch.1

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36: 13.6 Relations to Other Functions

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§13.6(vii) Coulomb Functions

►For representations of Coulomb functions in terms of Kummer functions see (33.2.4), (33.2.8) and (33.14.5).

37: 31.12 Confluent Forms of Heun’s Equation

… ►This has regular singularities at $z=0$ and $1$, and an irregular singularity of rank 1 at $z=\mathrm{\infty }$. ►Mathieu functions (Chapter 28), spheroidal wave functions (Chapter 30), and Coulomb spheroidal functions (§30.12) are special cases of solutions of the confluent Heun equation. …

38: Bibliography H

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Two-center Coulomb functions. Comput. Phys. Comm. 103 (2-3), pp. 209–216.

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Notes:

Double-precision Fortran code.

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ISSN 0010-4655, Document, Code

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6th item.

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Calculation of Coulomb wave functions for high energies. Phys. Rev. 54 (8), pp. 627–628.

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External Links:

Document

Referenced by:

§33.7.

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Coulomb Wave Functions. In Handbuch der Physik, Bd. 41/1, S. Flügge (Ed.), pp. 408–465.

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External Links:

MathReview (G. Källén)

Referenced by:

§33.2(iii), §33.23(vii), §33.23(vii), §33.24, §33.5(ii), §33.7, Ch.33.

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Analytical structure and properties of Coulomb wave functions for real and complex energies. Ann. Physics 155 (2), pp. 461–493.

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External Links:

ISSN 0003-4916, Document, MathReview

Referenced by:

§33.10(ii), §33.13, §33.22(vii).

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Bessel function expansions of Coulomb wave functions. J. Math. Phys. 26 (4), pp. 656–659.

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External Links:

ISSN 0022-2488, Document, MathReview, ZentralBlatt

Referenced by:

§33.10(ii), §33.10(iii), §33.14(iv), §33.9(ii), §33.9(ii).

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39: Bibliography Y

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Coulomb wave functions in repulsive fields. Phys. Rev. 49 (2), pp. 174–189.

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External Links:

Document, ZentralBlatt

Referenced by:

§33.10(i), §33.2(ii), §33.2(iii), §33.2(iv), §33.5(i), §33.5(iv), §33.9(ii).

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40: Bibliography S

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Coulomb functions analytic in the energy. Comput. Phys. Comm. 25 (1), pp. 87–95.

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Notes:

Double-precision Fortran code.

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Referenced by:

§33.1, §33.14(iv), 9th item.

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The accuracy of iterated JWBK approximations for Coulomb radial functions. Comput. Phys. Comm. 32 (2), pp. 115–119.

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Document

Referenced by:

§33.23(vii).

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Coulomb functions for attractive and repulsive potentials and for positive and negative energies. Comput. Phys. Comm. 146 (2), pp. 225–249.

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External Links:

ISSN 0010-4655, Document, MathReview, ZentralBlatt

Referenced by:

§1.17(ii), §33.1, §33.14(i), §33.14(ii), §33.14(iii), §33.14(iv), §33.14(v), §33.16(i), §33.16(ii), §33.16(iii), §33.16(v), §33.17, §33.19, §33.20(i), §33.20(ii), §33.20(iii), §33.21(i), Ch.33.

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FGH, a code for the calculation of Coulomb radial wave functions from series expansions. Comput. Phys. Comm. 146 (2), pp. 250–253.

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Notes:

Single-precision Fortran code.

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Referenced by:

10th item.

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NUMER, a code for Numerov integrations of Coulomb functions. Comput. Phys. Comm. 146 (2), pp. 254–260.

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Notes:

Single-precision Fortran code.

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Referenced by:

11st item.

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