I have an interest in finding the closed-form of numbers such as the reciprocal Fibonacci constant and $\zeta(2n+1)$.
I always refer to this as closed-form analysis, but is there a formal name for this kind of study already?
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3You could call yourself a "human algebra system". – Antonio Vargas Dec 14 '13 at 21:23
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A closed form also depends on which functions, etc, are defined/named giving a “manmade” component to what is a closed form. – Тyma Gaidash Jul 21 '22 at 20:04
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Until now, "closed-form analysis" itself seems not to be a field of study in mathematics. It is part of the single fields of mathematics. There are a lot of mathematical articles that describe closed forms for single applications and are titled with the term "closed-form analysis".
Closed forms are treated e.g. at antiderivatives, differential equations, equations, functions, generating functions, inverses, numbers, series. There are some concepts and methods for closed-forms in these fields.
see e.g.:
Wikipedia: Closed-form expression
Wikipedia: Closed-form expression - Closed-form number
Are there some techniques which can be used to show that a sum "does not have a closed form"?
[Chow 1999] Chow, T.: What is a closed-form number. Am. Math. Monthly 106 (1999) (5) 440-448
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