very general calculus tommy1729 Ultimate Fellow     Posts: 1,924 Threads: 415 Joined: Feb 2009 12/01/2010, 06:16 PM very general calculus ********************* from a [r] b = b [r] a = exp^[r]( exp^[-r](a) + exp^[-r](b) ) http://math.eretrandre.org/tetrationforu...hp?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 « Next Oldest | Next Newest »

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