# Zeta function Calculator

## Calculates the Riemann zeta functions ζ(x) and ζ(x)-1.

 x real number 6digit10digit14digit18digit22digit26digit30digit34digit38digit42digit46digit50digit
 $\normal Zeta\ function\ \zeta(x)\\[10](1)\ \zeta(x)= {\large\sum_{\small n=1}^ {\small\infty}\frac{1}{n^x}}\hspace{30}x\ge 1,\hspace{20}\zeta(1)=\infty\\(2)\ \zeta(2n)={\large\frac{2^{2n-1}\pi^{2n}|B_{2n}|}{(2n)!}}\hspace{30}{\normal n=1,2,3,...}\\(3)\ \zeta(-n)={\large\frac{B_{n+1}}{n+1}}\hspace{30}{\normal n=2,3,4,...}\\(4)\ \zeta(x)={\large\prod_{\small p:prime}\frac{1}{1-p^{-x}}}\hspace{30}{\normal Euler\ product}\\\hspace{120}B_n:Bernoulli\ number\\$
Zeta function
 [1-10] /21 Disp-Num5103050100200
[1]  2018/10/30 03:37   Female / Under 20 years old / High-school/ University/ Grad student / Very /
Purpose of use
college essay
[2]  2018/10/23 04:30   Male / Under 20 years old / High-school/ University/ Grad student / Very /
Purpose of use
Demonstrate that 1+2+3+4+5+6+7...=-1/12
[3]  2018/10/14 18:31   Male / 20 years old level / High-school/ University/ Grad student / Useful /
Purpose of use
I wanted to calibrate a specific calculator, and test the precision of multiple methods.
[4]  2018/10/01 04:02   Male / 50 years old level / A retired person / Useful /
Purpose of use
Curiosity
[5]  2018/09/09 06:02   Male / 60 years old level or over / A teacher / A researcher / A little /
Purpose of use
I wanted to calculate cumulative learning curve values for a quantitative methods class. I wanted the sum of a finite number of terms with s in the range .02 - .5
Comment/Request
There appeaars to be no way to limit the sum to a finite number of terms.
[6]  2018/05/30 03:23   Male / 30 years old level / An office worker / A public employee / Very /
Purpose of use
curiosity
[7]  2018/05/29 04:48   Male / Under 20 years old / Elementary school/ Junior high-school student / Useful /
Purpose of use
Recreation
[8]  2018/05/11 03:57   Male / Under 20 years old / Elementary school/ Junior high-school student / A little /
Purpose of use
fun
[9]  2017/12/22 05:42   Male / 60 years old level or over / A retired people / Very /
Purpose of use
to help discover the solution to millennium problem
[10]  2017/08/08 00:17   Female / Under 20 years old / High-school/ University/ Grad student / Not at All /
Purpose of use
calculate
Comment/Request
where can i type in imaginary numbers
from Keisan
This calculator does not support complex numbers.
=> ex) Select Mode "Complex RAD" and input "zeta(1+3i)"

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