Bernoulli polynomials

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Bernoulli polynomials - Namir - 2025-12-01 18:53

Here is the listing for a function that evaluates a Bernoulli polynomial of order n and for argument x.The calculations use a nested summation.

Code:
EXPORT BERNL(n,x)
BEGIN
  LOCAL k, m, sum1, sum2;
  LOCAL t1, t2;
 
  sum1:=0;
  FOR k FROM 0 TO n DO
    sum2:=0;
    FOR m FROM 0 TO k DO
      t2:=(-1)^m*COMB(k,m)*(x+m)^n;
      sum2:=sum2+t2;
    END;
    t1:=sum2/(k+1);
    sum1:=sum1+t1;
  END;
  RETURN sum1;
END;