I think Jay defined the constant 1.08... as the ratio of my functional equation f(x+1) - f(x) = f(x/2) with his J ' (x) = J(x/2).
Im not sure if he intended that.
It is consistant if my f(x) is very close the Original sequence a(x) in the sense lim x-> +oo f(x)/a(x) = 1.
( then it follows lim x-> + oo J(x)/a(x) = J(x)/f(x) = 1.08... )
I have the feeling Jay's post/idea is not complete yet or still under development , probably there will be an edit or a followup.
A little bit strange notation I think , but that might be due to the unfinished brainstorming too.
Anyway , thanks for the posts Jay !
I have to think about Jay's last post now.
My first critical remark is that the analogue for exp does not seem convincing right now ; I do not see (1+1/n)^n.
But I might need to read again and Jay will probably do an edit or followup. Its just a first impression anyway.
regards
tommy1729
EDIT : I was referring to Jay's post 30 mainly. He posted nr 31 while I made this reply.
Im not sure if he intended that.
It is consistant if my f(x) is very close the Original sequence a(x) in the sense lim x-> +oo f(x)/a(x) = 1.
( then it follows lim x-> + oo J(x)/a(x) = J(x)/f(x) = 1.08... )
I have the feeling Jay's post/idea is not complete yet or still under development , probably there will be an edit or a followup.
A little bit strange notation I think , but that might be due to the unfinished brainstorming too.
Anyway , thanks for the posts Jay !
I have to think about Jay's last post now.
My first critical remark is that the analogue for exp does not seem convincing right now ; I do not see (1+1/n)^n.
But I might need to read again and Jay will probably do an edit or followup. Its just a first impression anyway.
regards
tommy1729
EDIT : I was referring to Jay's post 30 mainly. He posted nr 31 while I made this reply.