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Apr
11
asked Is every natural recursive relation necessarily holomorphic?
Mar
28
asked Q Pochammer Symbol Product Identities
Mar
28
comment Infinite sum involving ascending powers
I have question, The sum that I gave above definitely converges for all x, if $a > 1$ and $a \in \Bbb{R}$ yet the expression you gave doesn't converge unless $|a|<1$ That suggests to me an analytic continuation is necessary. What is the analytic continuation I'm looking for?
Mar
21
accepted Artificial Integer?
Mar
21
comment Artificial Integer?
@ThomasAndrews Yep! I think you had the exact same line of thought back then as I am beginning to explore onw
Mar
21
comment Artificial Integer?
I wanted it to be as general as possible while still being consistent with the laws of modular arithmetic. In other words if $a \equiv b \mod N$ then $f(a) \equiv f(b) \mod N$ do there exist non polynomial functions that satisfy that?
Mar
21
comment Artificial Integer?
In the even the function is defined cleanly ${\Bbb{Z}}/{\Bbb{N}}$ does that change things significantly?
Mar
21
comment Artificial Integer?
How to reconcile these two? @Thomas Andrews
Mar
21
comment Artificial Integer?
See my comment underneath @ThomasAndrews for the tricky part with |x|
Mar
21
comment Artificial Integer?
I still have issues with the answer though, namely that $|x|$ isn't well behaved. I don't think this is the question I really mean to ask, but I'm trying to figure what question I should be asking. There needs to be restriction on f in this case
Mar
21
comment Artificial Integer?
I guess the trick is defining $|x|$ for the integers modulo N. For example $|-1| = 1$, yet $-1 \equiv 7 \mod 8 \rightarrow |-1| \equiv |7| \rightarrow 1 \equiv 7 \mod 8 $ and that is clearly no true
Mar
21
comment Artificial Integer?
This gives us $1 + |k| \mod R$ for some integer $0 \le k \le R-1$ and another integer $R$. There is not integer for which it is 0. But for every R there exists a k (namely R-1) such that is 0. Ah! thats a good one :)
Mar
21
revised Artificial Integer?
added 7 characters in body
Mar
21
asked Artificial Integer?
Mar
20
revised reduction formulae for $\int_0^1 (x^{\frac{n+2}2}\sqrt{1-x})dx\,\!$
edited tags
Mar
20
comment Do there exist Artificial Squares?
This was very clean. What was your motivation behind this particular strategy :)
Mar
20
accepted Do there exist Artificial Squares?
Mar
20
comment Do there exist Artificial Squares?
Ah yes, that reminds me
Mar
20
asked Zeroes of Jacobi Theta Functions
Mar
20
comment How to find the sum
Welcome to Math.SE! Please show whar have you tried so far on the problem. If you show some work it will help considerably in getting more views and answers :)