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> There is some argument to be made for exp, as it is considered an 'elementary function'. But exp() is defined as the limit over an infinite sum, so why does
by adwn 6y ago
> There is some argument to be made for exp, as it is considered an 'elementary function'.
But exp() is defined as the limit over an infinite sum, so why does it get to be an elementary function?
My point it that the distinction between closed form and non-closed form is arbitrary, and that there is no qualitative difference. In fact, limit and integral are just (higher-order) functions as well – and rather ubiquitous ones, so why aren't they considered elemental?
- redis_mlc 6y agoYou're not wrong, in that closed-form is not a clearly-defined term. However, mathematicians rarely do numerical calculations, so exp(), gamma, etc. are considered elementary functions, and there's no urgency to translate from symbols to numbers. Physicists who do calculations might be more restrictive about what closed-form means if they intend to compute a numeric result. https://en.wikipedia.org/wiki/Closed-form_expression https://en.wikipedia.org/wiki/Closed-form_expression Source: I studied pure mathematics, and we never used calculators - it was laughable, in fact. Most of our series never converged in the first place. :)