Pochhammer symbols

[rwst]

While Sage already has falling_factorial and rising_factorial functions they are not symbolic. Always using gamma or product expansions may be inconvenient in some cases, and does not offer the option to rewrite expressions in terms of them. Especially the product form cannot be easily rewritten as gamma expression. So the product expansion should be made optional.

Component: symbolics

Keywords: falling_factorial, rising_factorial

Issue created by migration from https://trac.sagemath.org/ticket/19461

[arminstraub]

comment:1

It seems that this has been fixed in recent versions of Sage. At least, the functions can now be used as part of symbolic expressions:

sage: rising_factorial(x, 3)
(x + 2)*(x + 1)*x
sage: rising_factorial(x, x)
gamma(2*x)/gamma(x)

I have therefore set the ticket to "invalid". Please change back if I am misreading the description.

[arminstraub]

comment:2

On another ticket I was told to also set these to positive review... If that's not universally true, please let me know.

[arminstraub]

Reviewer: Armin Straub

[rwst]

comment:3

Replying to @arminstraub:

It seems that this has been fixed in recent versions of Sage. At least, the functions can now be used as part of symbolic expressions:

sage: rising_factorial(x, 3)
(x + 2)*(x + 1)*x
sage: rising_factorial(x, x)
gamma(2*x)/gamma(x)

It was not fixed. I would like at least the option of not converting to gamma fractions, which is impossible without a symbolic function. Also, you don't want rising_factorial(x, 3000) expanded. The function itself is worthwhile to have.

On another ticket I was told to also set these to positive review.

I think this applies only to tickets that you have started.

[rwst]

Changed reviewer from Armin Straub to none