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Nemocas / Nemo.jl

Julia bindings for various mathematical libraries (including flint2)
http://nemocas.github.io/Nemo.jl/
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Series expansion to 1F1 #540

Open edwardcao3026 opened 5 years ago

edwardcao3026 commented 5 years ago

Can anyone advise how to do series expansion to a product of confluent hypergeometric functions 1F1(a, b, x)*1F1(c, d, x) using Nemo? Thanks.

wbhart commented 5 years ago

At the moment this is certainly not implemented. Though perhaps someone else knows a way of getting it without a lot of work.

fredrik-johansson commented 5 years ago

With a C call, there is acb_hypgeom_pfq_series_direct.

fredrik-johansson commented 5 years ago

Though, in this specific case, you might be better off computing the terms of the 1F1 series using recurrence relations.

edwardcao3026 commented 5 years ago

Do you mind sharing more details about the C call method?

wbhart commented 5 years ago

The C function in Arb is documented here:

wbhart commented 5 years ago

http://arblib.org/acb_hypgeom.html

But from memory we only wrap acb_poly and do not have an acb_series module in Nemo yet. We only have generic series over acb's, I think. And I think the former would really be required to wrap the C function.

Of course you could hack something together, but I assume you will want to do something with it, not just compute it and look at it.

edwardcao3026 commented 5 years ago

The link is not displayed...

wbhart commented 5 years ago

Yeah sorry, I tried to press SHIFT-ENTER, but pressed some other swizzlestick by mistake. The link is in the next comment.