Implement Krawtchouk, Meixner, and Hahn polynomials

[tscrim]

These are three classes of orthogonal polynomials in
the Askey scheme.
We should provide an implementation based on
their definition as hypergeometric functions.

This ticket provides just a basic implementation with
no particular reason for the normalization choices.

CC: @dimpase @sagetrac-tmonteil @ferihr @fchapoton @mezzarobba @slel

Component: symbolics

Keywords: orthogonal polynomials

Author: Travis Scrimshaw

Branch/Commit: 9b40ec4

Reviewer: Frédéric Chapoton

Issue created by migration from https://trac.sagemath.org/ticket/33393

[tscrim]

comment:1

An implementation of the Krawtchouk polynomials appear in coding/delsarte_bounds.py. I am cc-ing those people as they might be interested (at least for consistency such as normalization differences and/or possible cross-references). This code is likely slower as it is more general but I haven't checked.

---

New commits:

9b5f2e1	Cleanup functions/orthogonal_polys.py.
6dca173	Adding krawtchouk polynomials.
cb7a54c	Adding Meixner polynomials; fixing some details with Krawtchouk.
9399347	Implement Hahn polynomials.

[tscrim]

Branch: public/symbolics/more_orthogonal_polys-33393

[tscrim]

Commit: 9399347

[fchapoton]

comment:2

the "eval_recursive" should be cached (in parent ?), don't you think ?

[tscrim]

comment:3

There isn't really a parent per se. Since the input could be widely varied, it doesn't make so much sense to cache it (and could quick eat up memory). There might be some benefit to caching the resulting (generic) polynomial, but this would likely need a bit of refactoring.

[sagetrac-git]

Changed commit from 9399347 to b9f1eef

[sagetrac-git]

Branch pushed to git repo; I updated commit sha1. New commits:

b9f1eef

eval_recursive() is a method, not a function.

[tscrim]

comment:6

This fixes the pyflakes issues reported by the otherwise green patchbot.

[sagetrac-git]

Changed commit from b9f1eef to cc6feca

[sagetrac-git]

Branch pushed to git repo; I updated commit sha1. New commits:

f3e2af0	Merge branch 'public/symbolics/more_orthogonal_polys-33393' of https://github.com/sagemath/sagetrac-mirror into public/symbolics/more_orthogonal_polys-33393
cc6feca	Some little documentation tweaks and improvements.

[sagetrac-git]

Branch pushed to git repo; I updated commit sha1. New commits:

2c45db3

Some additional document improvements, including some more history.

[sagetrac-git]

Changed commit from cc6feca to 2c45db3

[tscrim]

comment:9

Patchbot is (morally) green.

[fchapoton]

comment:10

ok

maybe one could add cross-references from and to the Krawtchouk polynomials in coding ?

[dimpase]

comment:11

Replying to @fchapoton:

ok

maybe one could add cross-references from and to the Krawtchouk polynomials in coding ?

perhaps on a follow-up ticket?

[sagetrac-git]

Changed commit from 2c45db3 to b0154c5

[sagetrac-git]

Branch pushed to git repo; I updated commit sha1. New commits:

7a20625	Merge branch 'develop' into public/symbolics/more_orthogonal_polys-33393
b0154c5	Adding crossrefs and a bit more documentation.

[tscrim]

comment:13

I think that is a good idea to have crossrefs. I have added them along with an explicit test checking the relationship between the conventions.

[fchapoton]

comment:14

ok, thenl let's go

[fchapoton]

Reviewer: Frédéric Chapoton

[tscrim]

comment:15

Thank you.

[vbraun]

comment:16

[sagemath_doc_pdf-none] ? 
[sagemath_doc_pdf-none] ! Emergency stop.
[sagemath_doc_pdf-none]  ...                                              
[sagemath_doc_pdf-none]                                                   
[sagemath_doc_pdf-none] l.4558 They are named after Pafnuty Chebyshev (Ч
[sagemath_doc_pdf-none]                                                  ебышёв 1821\sphinxhyp...
[sagemath_doc_pdf-none] 

[tscrim]

comment:17

It looks like the pdf doc doesn’t like Cyrillic so much; I thought it would be fine with the Russian tutorial. Do you know how to get that to work? If not, then we can just remove it.

[fchapoton]

comment:18

just remove cyrillic

[sagetrac-git]

Branch pushed to git repo; I updated commit sha1. New commits:

9b40ec4

Remove Cyrillic from doc so pdf will compile.

[sagetrac-git]

Changed commit from b0154c5 to 9b40ec4

[tscrim]

comment:20

Removed.

[fchapoton]

comment:22

did you check that pdf doc compiles ?

[tscrim]

comment:23

Yes, the pdf doc compiles for me.

[fchapoton]

comment:24

Thanks, then let's move on

[vbraun]

Changed branch from public/symbolics/more_orthogonal_polys-33393 to 9b40ec4