Hello,
A quick query. Have adapted existing Matlab code for Scilan to calculate
Bernoulli numbers using an explicit formula (www.bernoulli.org). The code
works fine for numbers from 0 to 10, but 11 onwards the values are
incorrect:
Not the most efficient code but do need to understand where the errors are
coming in.
clear
function Binomial_coefficient=bcoeff(n,k)
Binomial_coefficient=factorial(n)/(factorial(k)*factorial(n-k))
endfunction
B=[];
for m=0:20
sum2=0;
for k=0:m
sum1=0;
for v=0:k
sum1=sum1+ (((-1)^v)*bcoeff(k,v)*(v^m)/(k+1));
end
sum2=sum2+sum1;
end
B(m+1)=sum2;
end
Output of B(n) for 0 to 20 (left column), right column = expected values;
note B(7) and B(9) show rounding issues*
1.
-0.5
0.1666667
0.
-0.0333333
0.
0.0238095
7.503D-12* 0.0
-0.0333333
2.215D-08* 0.0
0.0757573
0.0000024 0.0
-0.2520505 −0.253113553
-0.0072098 0.0
1.2467346 +1.166666666
-12.6875 0.0
-827.875 −7.092156862
12752.25 0.0
-2091400. +54.97117794
2.104D+09 0.0
6.417D+10 −529.1242424
Also, is it possible to print/write values in a more readable form, e.g.:
B(0) = 1
B(1) = -0.5
...etc
B(20) = −529.1242424
Thanks for any pointers
Lester
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