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]

Description changed:

--- 
+++ 
@@ -1 +1,3 @@
 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.

[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.

[slel]

Description changed:

--- 
+++ 
@@ -1,3 +1,7 @@
-These are three classes of orthogonal polynomials in the Askey scheme. We should provide an implementation based on their definition as hypergeometric functions.
+These are three classes of orthogonal polynomials in
+the [Askey scheme](https://en.wikipedia.org/wiki/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.
+This ticket provides just a basic implementation with
+no particular reason for the normalization choices.

[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.