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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