2 Apr
2014
2 Apr
'14
3:19 p.m.
how could we tell?
wikipedia: It has been proved that GAMMA(n+r) is a transcendental number and algebraically independent of pi for any integer n and each of the fractions r = 1/6, 1/4, 1/3, 2/3, 3/4, and 5/6. citing: http://www.math.jussieu.fr/~miw/articles/pdf/TranscendencePeriods.pdf which used the connection to elliptic functions. more generally, if you had algebraic or rational independence results you "could tell." Other papers: http://www-fourier.ujf-grenoble.fr/~rivoal/articles/gammater.pdf http://www.mast.queensu.ca/~murty/gun-murty-rath2.pdf in particular note Nesterenko's theorem in the latter.