very general calculus - Printable Version +- Tetration Forum (https://tetrationforum.org) +-- Forum: Tetration and Related Topics (https://tetrationforum.org/forumdisplay.php?fid=1) +--- Forum: Hyperoperations and Related Studies (https://tetrationforum.org/forumdisplay.php?fid=11) +--- Thread: very general calculus (/showthread.php?tid=543) |
very general calculus - tommy1729 - 12/01/2010 very general calculus ********************* from a [r] b = b [r] a = exp^[r]( exp^[-r](a) + exp^[-r](b) ) http://math.eretrandre.org/tetrationforum/showthread.php?tid=520 " the distributive property " it follows that a generalization of infinite sums and infinite products in calculus is f(z) = [ Tommy r ] ( exp^[r](1) + a_i z^n ) where [ Tommy r ] means [ Tommy r ] b_i = b_0 [r] b_1 [r] b_2 [r] b_3 [r] ... for instance f(z) = [ Tommy -1 ] ( 0 + a_i z^n ) is a power series. f(z) = [ Tommy 0 ] ( 1 + a_i z^n ) is the infinite product of ( 1 + a_i z^n) defined for abs z at most 1. and in general for r > 0 f(z) = [ Tommy r ] ( exp^[r](1) + a_i z^n ) defined for abs z at most exp^[r](1). tommy1729 |