If this is possible, how would I go about proving this? It's ok for the function to be defined in multiple variables and use multiple integrals, given that the domain itself is also defined by rational functions.
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Perhaps you could say something about why you think that this might/should be the case? – joriki Feb 01 '20 at 11:41
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1https://en.wikipedia.org/wiki/Ring_of_periods The definition of a period says that it's the integral of a algebraic function over an algebraic domain. I don't know why this would be the case, but I was just wondering if the word "algebraic" could be reduced to "rational" and have it still work. – intingfeeder Feb 02 '20 at 03:56
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Do you have an example of an irrational algebraic number that can be expressed in this way? My cursory attempts at finding such an expression failed; I always get either a rational number or a number that's likely transcendental. – joriki Feb 02 '20 at 11:54