kevin lucas on Sat, 27 Jan 2018 22:44:45 +0100


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Finding Closed Form Repesentations from Truncated Decimal Expansions


Hello all,

I sometimes come across papers or talks in which PARI/GP is said to have been used to establish or conjecture complicated integer relations, often with a handwavy reference to LLL. I cannot, however, find an explicit demonstration for even simple algebraic closed forms like (1+sqrt(5))/2. How, for instance, could PARI find for 0.22004376711264303785068975981048665667...  the closed form (1+sqrt(2))^2/(2^(9/4)*Pi^(3/2))? Secondly, how can one incorporate more exotic constants into the process, like multiple zeta values or values of certain L-functions? Any help or references would of course be highly appreciated.

Sincerely,
Kevin Lucas