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Pochhammer symbols #19461
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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:
I have therefore set the ticket to "invalid". Please change back if I am misreading the description. |
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. |
Reviewer: Armin Straub |
comment:3
Replying to @arminstraub:
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
I think this applies only to tickets that you have started. |
Changed reviewer from Armin Straub to none |
comment:4
Replying to @rwst:
I would disagree on that part. If I ever do explicitly write Also note that we can express the Pochhammers using binomial coefficents. And,
That's of course a different matter. Maybe you could update the description? (The part after "i.e." and the second sentence about implementations like Gosper do not apply anymore.)
I see, thanks! |
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Changed keywords from none to falling_factorial, rising_factorial |
comment:7
Replying to @arminstraub:
Actually it does apply. Gosper's and similar algorithms need to transform expressions to gamma expressions, and that's very simple with a |
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comment:9
The planned behaviour would be expanding as the default. Adding However, it seems at first the ticket cannot be implemented unless matrices etc. coerce into SR:
The reason is that making the symbolic The pragmatic solution would be to accept there are two versions of the functions |
While Sage already has
falling_factorial
andrising_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
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