Tetration Forum
very general calculus - Printable Version

+- Tetration Forum (https://math.eretrandre.org/tetrationforum)
+-- Forum: Tetration and Related Topics (https://math.eretrandre.org/tetrationforum/forumdisplay.php?fid=1)
+--- Forum: Mathematical and General Discussion (https://math.eretrandre.org/tetrationforum/forumdisplay.php?fid=3)
+--- 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