• 0 Vote(s) - 0 Average
• 1
• 2
• 3
• 4
• 5
 very general calculus tommy1729 Ultimate Fellow     Posts: 1,358 Threads: 330 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 »

 Possibly Related Threads... Thread Author Replies Views Last Post Isomorphism of newtonian calculus rules for Non-Newtonian (anti)derivatives of hypers Micah 4 1,427 03/02/2019, 08:23 PM Last Post: Micah A calculus proposition about sum and derivative tommy1729 1 1,943 08/19/2016, 12:24 PM Last Post: tommy1729 Fractional calculus and tetration JmsNxn 5 7,223 11/20/2014, 11:16 PM Last Post: JmsNxn Theorem in fractional calculus needed for hyperoperators JmsNxn 5 6,530 07/07/2014, 06:47 PM Last Post: MphLee General question on function growth dyitto 2 3,965 03/08/2011, 04:41 PM Last Post: dyitto general sums tommy1729 5 6,581 06/24/2010, 07:56 PM Last Post: kobi_78 some general thoughts Gottfried 8 8,513 01/06/2010, 07:38 AM Last Post: Gottfried properties of abel functions in general Base-Acid Tetration 3 5,189 10/24/2009, 10:10 AM Last Post: bo198214 question about regular iteration, also about tetration properties in general Base-Acid Tetration 6 8,314 05/10/2009, 09:32 AM Last Post: bo198214

Users browsing this thread: 1 Guest(s) 