This resource function is obsolete. Use the function CoulombF instead.

Function Repository Resource:

# CoulombF

Evaluate the regular Coulomb wavefunction

Contributed by: Jan Mangaldan
 ResourceFunction["CoulombF"][l,η,ρ] gives the regular Coulomb wavefunction Fl(η,ρ).

## Details

Mathematical function, suitable for both symbolic and numerical manipulation.
Fl(η,ρ) satisfies the Coulomb wave differential equation ρ2{ρ,2}w+(ρ2-2ηρ-l(l+1))w=0.
For certain special arguments, ResourceFunction["CoulombF"] automatically evaluates to exact values.
ResourceFunction["CoulombF"] can be evaluated to arbitrary numerical precision.

## Examples

### Basic Examples (3)

Evaluate numerically:

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Plot F0(-2,ρ) over a subset of the reals:

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Series expansion at the origin:

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### Scope (4)

Evaluate for complex arguments:

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Evaluate to high precision:

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The precision of the output tracks the precision of the input:

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Simple exact values are generated automatically:

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### Applications (1)

Plot CoulombF as a function of ρ and η:

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### Properties and Relations (3)

CoulombF satisfies a differential equation:

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CoulombF satisfies a recurrence relation:

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Express the derivative of CoulombF in terms of CoulombF:

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## Version History

• 1.1.0 – 13 September 2021
• 1.0.0 – 03 March 2021