Euler Polynomial

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Euler Polynomial - Namir - 2025-12-01 18:53

Here is a listing for the Euler polynomials of order n and argument x:  The calculations use a nested summation.

Code:
EXPORT EULR(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:=sum2/2^k;
     sum1:=sum1+t1;
   END;
   RETURN sum1;
END;