Results of Coulomb Functions

Notation

33.1 Special Notation

Variables ${\displaystyle{\displaystyle\rho,\eta}}$

33.2 Definitions and Basic Properties
33.3 Graphics
33.4 Recurrence Relations and Derivatives
33.5 Limiting Forms for Small ${\displaystyle{\displaystyle\rho}}$ , Small ${\displaystyle{\displaystyle|\eta|}}$ , or Large ${\displaystyle{\displaystyle\ell}}$
33.6 Power-Series Expansions in ${\displaystyle{\displaystyle\rho}}$
33.7 Integral Representations
33.8 Continued Fractions
33.9 Expansions in Series of Bessel Functions
33.10 Limiting Forms for Large ${\displaystyle{\displaystyle\rho}}$ or Large ${\displaystyle{\displaystyle\left|\eta\right|}}$
33.11 Asymptotic Expansions for Large ${\displaystyle{\displaystyle\rho}}$
33.12 Asymptotic Expansions for Large ${\displaystyle{\displaystyle\eta}}$
33.13 Complex Variable and Parameters

Variables ${\displaystyle{\displaystyle r,\epsilon}}$

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 ${\displaystyle{\displaystyle\ell}}$
33.19 Power-Series Expansions in ${\displaystyle{\displaystyle r}}$
33.20 Expansions for Small ${\displaystyle{\displaystyle|\epsilon|}}$
33.21 Asymptotic Approximations for Large ${\displaystyle{\displaystyle|r|}}$

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