(50g) Bernoulli polynomials

[peacecalc]

Hello folks,

now I have the summation function \GS replaced by FOR NEXT loops:

Input is n and the variable for the polynomials 'X'

Code:


« 0 DUP \-> M X RSI RSO
  « 0 M
    FOR N 1 N + INV 0 N 0 'RSI' STO
      FOR K -1 K ^ N K COMB * X K + M ^ * 'RSI' STO+
      NEXT RSI * 'RSO' STO+
    NEXT RSO EVAL FDISTRIB 
  »
»

For getting a symbolic calculation it is necessary to use integer values for the loops (although floatings has a faster performance).

Nice comparison, the "integral" code is slower until n = 18 or 19 and the "sum" code is faster. For n greater or equal 20 the tide turned, the "integral" code is faster (although it uses the CAS-functions "INTVX", "ISOL" and "SUBTL")...
The summations goes quatric with n...

greetings
peacecalc