Reputation
2,025
Top tag
Next privilege 2,500 Rep.
Create tag synonyms
Badges
1 9 22
Impact
~34k people reached

1d
revised Non-standard numbers and exponential form of Zeta function
deleted 4 characters in body
2d
revised Non-standard numbers and exponential form of Zeta function
added 4 characters in body
2d
revised Non-standard numbers and exponential form of Zeta function
added 46 characters in body
2d
revised Non-standard numbers and exponential form of Zeta function
deleted 313 characters in body
2d
revised Non-standard numbers and exponential form of Zeta function
added 2 characters in body
2d
revised Non-standard numbers and exponential form of Zeta function
added 288 characters in body
2d
asked What function is this? $\sum_{k=0}^\infty \frac{2^{2k}z^{2k-1}}{(2k)!}$
2d
accepted What is the sum of this series? $\sum_{n=1}^\infty\frac{\zeta(1-n)(-1)^{n+1}}{2^{n-1}}$
2d
comment Non-standard numbers and exponential form of Zeta function
@mercio I highly appreciate your criticism and I found the mistake. I have corrected the formulas and pictures so now it should work well. $4(\omega_-)^2+0+(-1/2)+(-1/2)=4\tau^2$. The formulas for the exponentiation are now simplier in that they use simply Bernoulli numbers. And also it seems a more general formula works, $\operatorname{st}(\tau+y)^x=-x\zeta(1-x,1/2-y)$ although I should verify it. If so, the whole role of Hurwitz Zeta becomes clear.
2d
revised Non-standard numbers and exponential form of Zeta function
added 37 characters in body
2d
revised Non-standard numbers and exponential form of Zeta function
edited body
2d
revised Non-standard numbers and exponential form of Zeta function
deleted 51 characters in body
Aug
29
comment Non-standard numbers and exponential form of Zeta function
@mercio what do u mean?
Aug
29
comment Non-standard numbers and exponential form of Zeta function
@mercio the number of Gaussian integers with positive real and imaginary parts not exceeding n (6th picture) is n(n+1)/2 which is partial sum of 1+2+3+4+... en.wikipedia.org/wiki/1_%2B_2_%2B_3_%2B_4_%2B_%E2%8B%AF
Aug
29
comment What is the sum of this series? $\sum_{n=1}^\infty\frac{\zeta(1-n)(-1)^{n+1}}{2^{n-1}}$
Now I fixed the problem. Sorry. In this form it is exactly what I want.
Aug
29
revised What is the sum of this series? $\sum_{n=1}^\infty\frac{\zeta(1-n)(-1)^{n+1}}{2^{n-1}}$
added 3 characters in body; edited title
Aug
29
comment What is the sum of this series? $\sum_{n=1}^\infty\frac{2^n (-1)^{n+1} B_n}{n}$
@Daniel Fischer it came from there but modified. I just explained why there are no factorials.
Aug
29
asked What is the sum of this series? $\sum_{n=1}^\infty\frac{\zeta(1-n)(-1)^{n+1}}{2^{n-1}}$
Aug
29
comment What is the sum of this series? $\sum_{n=1}^\infty\frac{2^n (-1)^{n+1} B_n}{n}$
@michaelrccurtis it came from Maclauren's expansion for $1/(x + 1/2)$
Aug
29
comment What is the sum of this series? $\sum_{n=1}^\infty\frac{2^n (-1)^{n+1} B_n}{n}$
@Daniel Fischer well I would be OK with any of the summation methods, such as mean vanues etc.