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[Axiom-math] (n+1)! = n! * (n+1)
From: |
panaxiom |
Subject: |
[Axiom-math] (n+1)! = n! * (n+1) |
Date: |
Wed, 26 Dec 2018 21:56:26 +0100 |
User-agent: |
Horde Application Framework 5 |
Hi,
how can such definitons like factorial or other products be calculated
in a way,
that allows transformations like that, mentioned in the subject?
(I would like to have both directions.)
How can other formulas be handled in a (meta-?)symbolic way,
for example iterations on functions and derivatives handling with index-values
from 1 to n, with "..." for the parts between 1 and n in formulas.
What is needed, is things like Sum-formulas, for example Taylor of a
function f,
and the sum not with \sum symbol but with f^{(1)}, f^{(2)}, ..., f^{(n)},
and if I would use derivative of that taylor term, then the
derivation-index is changed accordingly.
Is such things possible?
Can the factorial-example be done with built-in functions?
or with recursive definitions of user-specific functions?
Any way to handle such things with axiom?
It would make some proofs (induction), which habe a lot of factorial-terms
or the above mentioned sum terms, easier to devleop adn write down
intuitively.
TIA,
pan
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panaxiom <=