# Bernoulli number Calculator

## Calculates the Bernoullis numbers Bn .

 Bn is a coefficient of the nth term of Taylor expansion of the generating function x/(ex-1).
 degree n n=0,1,2,... 6digit10digit14digit18digit22digit26digit30digit34digit38digit42digit46digit50digit Bn
 $\normal Bernoulli\ number\ B_n\\[10](1)\ {\large\frac{x}{e^x-1}}={\large\sum_{\small n=0}^ {\small\infty}\frac{B_n}{n!}}x^n\\\hspace{60}=B_0+{\large\frac{B_1}{1!}}x+{\large\frac{B_2}{2!}}x^2+...+{\large\frac{B_n}{n!}}x^n+...\\[10](2)\ B_n={\large\sum_{\small k=0}^ {\small n}\frac{1}{k+1}\sum_{\small j=0}^ {\small k}}(-1)^j\ _k C_j j^n\\[10]\hspace{30} B_{2n+1}=0\hspace{15}for\ n=1,2,...\\[10](3)\ B_0=1,\ B_1=-{\large\frac{1}{2}},\ B_2={\large\frac{1}{6}},\ B_4=-{\large\frac{1}{30}},\ ...\\$
Bernoulli number
 [1-1] /1 Disp-Num5103050100200
[1]  2013/07/19 15:37   Male / 40 years old level / An office worker / A public employee / Very /
Purpose of use
use it to update my residual knowledge

Sending completion

To improve this 'Bernoulli number Calculator', please fill in questionnaire.
Male or Female ?
Male Female
Age
Under 20 years old 20 years old level 30 years old level
40 years old level 50 years old level 60 years old level or over
Occupation
Elementary school/ Junior high-school student
High-school/ University/ Grad student A homemaker An office worker / A public employee
Self-employed people An engineer A teacher / A researcher
A retired person Others
Useful?
Very Useful A little Not at All
Purpose of use?