Why no ₁F₁?

Question

Why no ₁F₁?

dlfivefifty opened this issue 4 years ago · comments

Or M or U?

What's drummond1F1?

# ₁F₁(α,β;z)
function drummond1F1(α::T1, β::T2, z::T3; kmax::Int = 10_000) where {T1, T2, T3}

Mikael Slevinsky · Answer 1 · Tue Sep 08 2020 22:23:46 GMT+0800 (China Standard Time)

Could be added, though exporting single capital letters seems fraught. At some point, I thought it best to funnel all usage through pFq.

drummond1F1 is a rational approximation algorithm to 1F1. For pFq with p <= q, the Drummond algorithm is anecdotally stable.

Sheehan Olver · Answer 2 · Tue Sep 08 2020 22:30:18 GMT+0800 (China Standard Time)

No need to export: I think HypergeometricFunctions.M is very clean

Mikael Slevinsky · Answer 3 · Tue Sep 08 2020 22:38:50 GMT+0800 (China Standard Time)

Probably M can be added immediately. For U, I think we can use its representation as a linear combination of Ms and rationally approximate its asymptotic expansion, 2F0, via wenigerpFq.

Mikael Slevinsky · Answer 4 · Wed Dec 15 2021 23:50:34 GMT+0800 (China Standard Time)

_₁F₁(a, b, z) and HypergeometricFunctions.M(a, b, z) are added and special cased in pFq.