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Chapter 33 Coulomb Functions

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Acknowledgments:
This chapter is based in part on Abramowitz and Stegun (1964, Chapter 14) by M. Abramowitz.
Notes:
The main references used in writing this chapter are Hull and Breit (1959), Thompson and Barnett (1986), and Seaton (2002a). For additional bibliographic reading see also the General References in Chapter 13.
Referenced by:
§13.28(ii), Ian J. Thompson, § ‣ § Software Cross Index
Permalink:
http://dlmf.nist.gov/33
I. J. Thompson
Lawrence Livermore National Laboratory, Livermore, California.
   
  • Notation
    • 33.1 Special Notation
  • Variables \rho,\eta
    • 33.2 Definitions and Basic Properties
    • 33.3 Graphics
    • 33.4 Recurrence Relations and Derivatives
    • 33.5 Limiting Forms for Small \rho, Small |\eta|, or Large \ell
    • 33.6 Power-Series Expansions in \rho
    • 33.7 Integral Representations
    • 33.8 Continued Fractions
    • 33.9 Expansions in Series of Bessel Functions
    • 33.10 Limiting Forms for Large \rho or Large \left|\eta\right|
    • 33.11 Asymptotic Expansions for Large \rho
    • 33.12 Asymptotic Expansions for Large \eta
    • 33.13 Complex Variable and Parameters
  • Variables r,\epsilon
    • 33.14 Definitions and Basic Properties
    • 33.15 Graphics
    • 33.16 Connection Formulas
    • 33.17 Recurrence Relations and Derivatives
    • 33.18 Limiting Forms for Large \ell
    • 33.19 Power-Series Expansions in r
    • 33.20 Expansions for Small |\epsilon|
    • 33.21 Asymptotic Approximations for Large |r|
  • Physical Applications
    • 33.22 Particle Scattering and Atomic and Molecular Spectra
  • Computation
    • 33.23 Methods of Computation
    • 33.24 Tables
    • 33.25 Approximations
    • 33.26 Software
© 2010–2012 NIST / Privacy Policy / Disclaimer / Feedback; Version 1.0.5; Release date 2012-10-01 Math-Image version (See MathML) . A Printed Companion is available. ⇐ 32.17 Methods of Computation33.1 Special Notation ⇒