Chu-Vandermonde simplification fails

[fchapoton]

Simplification fails as follows:

sage: a, b, n = SR.var('a, b, n')
sage: A = hypergeometric([-n, a], [b], 1)
sage: assume(n, 'integer')
sage: assume(n > 0)
sage: A.simplify_hypergeometric()
    n
(-1) ⋅RisingFactorial(a - b - n + 1, n)
───────────────────────────────────────
	    pochhammer(b, n)

Note that Sage neither has RisingFactorial
or pochhammer as symbolic functions.
It does have a function "rising_factorial".

There is a sub-problem:

sage: jacobi_P(n, b, a, 1)
RisingFactorial(b + 1, n)
─────────────────────────
	    n!

CC: @slel @tscrim

Component: symbolics

Keywords: hypergeometric

Author: Frédéric Chapoton

Branch/Commit: e201391

Reviewer: Travis Scrimshaw

Issue created by migration from https://trac.sagemath.org/ticket/31299

[mkoeppe]

comment:2

Moving to 9.4, as 9.3 has been released.

[fchapoton]

comment:4

We need to register something somewhere...

sage: from sage.symbolic.expression import register_symbol
sage: register_symbol(rising_factorial, {'maxima': 'pochhammer'})
sage: d=maxima('pochhammer(x,y)')
sage: SR(d)
gamma(x + y)/gamma(x)

And then one stumbles on the fact that rising_factorial is not a symbolic function:

sage: var('n')
sage: assume(n, 'integer')
sage: assume(n > 0)
sage: rising_factorial(6,n)
BOOM

Maybe this should not test a.is_integer() but a in ZZ ?

[fchapoton]

Commit: 8f3f953

[fchapoton]

comment:5

here is a tentative, seems to work a little bit, but not completely

---

New commits:

8f3f953

tentative to convert pochhammer symbols from maxima

[fchapoton]

Branch: u/chapoton/31299

[slel]

comment:6

See also #19461.

[sagetrac-git]

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

f3fcdf2

pochhammer for dummies

[sagetrac-git]

Changed commit from 8f3f953 to f3fcdf2

[fchapoton]

comment:8

un peu mieux

[fchapoton]

comment:9

maybe it's a good start ?

[fchapoton]

Author: Frédéric Chapoton

[tscrim]

comment:12

I feel like it would be better to represent it as a ratio of Gamma functions considering how they appear in hypergeometric functions. Granted, it is a bit more computationally intensive for real x and integer n, but it allows the most general input. Plus it is consistent with Maxima in comment:4.

[sagetrac-git]

Changed commit from f3fcdf2 to e201391

[sagetrac-git]

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

12b458b	Merge branch 'u/chapoton/31299' in 9.5.b9
e201391	using gamma quotients to stand for pochhammer

[fchapoton]

comment:14

now with gamma

[tscrim]

Reviewer: Travis Scrimshaw

[tscrim]

comment:15

Thank you. LGTM.

[vbraun]

Changed branch from u/chapoton/31299 to e201391