Threaded Mode | Linear Mode

peacecalc · (This post was last modified: 12-17-2018 10:10 PM by peacecalc.)

Hello HP50g-fans,

I made a program for Bernoulli-polynomials ( = BP), it works with three equations:

\[ B_o(x) = 1 ~~~~~~~ \text{start}\]

\[ B_n(x) = n \cdot \int B_{n-1}(t)dt ~~~~~~~ \text{recursive definition}\]

\[ \int_0^1 B_n(t)dt = 0 ~~~~~~~~ \text{ calculate the constant from second equation}\]

Therefore we have polynomials it is easy to program and make use of CAS of the HP50g.
The program "BCALC" has to possibilities to work:

a) with one parameter "N", then it will calculate all BP from 0 to N, but it only stores the last N'th BP.

b) with two parameters "K" to "N". Let us say you calculated BP for N = 5, then you decide to calculate further on to N = 7. If you don't delete the global variables "BN1" and "BN2", you can input 6 and 7 and you get BP for N=7 from N = 5 as first equation.
That is a advantage in time, because the CAS operations are very slow.

To let the program know how many parameters I input, I use a list with one or two elements.

The program uses only one integration because the second one (stored in "BN2") prepares the BP for "N+1" (again time saving). I only make comments for the first part, I hope the rest of the program is understandable for you.

Code:

%%HP: T(2)A(R)F(.);

« OBJ->  

  IF 2. ==

  THEN \-> K N

    « K N FOR J 

            BN2 J * 'C' + EVAL DUP 'BN1' STO   @@RCL the prepared BP 

                                                            @@ and multiplied with J 

                                                            @@ add the constant "C" and stored

                                                            @@in BN1 temporally

            INTVX EVAL DUP 'BN2' STO            @@ integrated BP and stored

                                                            @@in BN2 temporally

            'X=1' SUBST EVAL 0 = 'C' ISOL DUP @@ set the upper limit 1 and calculate

                                                            @@ the constant "C"

            BN1 SWAP SUBST EVAL FDISTRIB   @@ RCL the BN1 und substitute the "C"

            'BN1' STO                                   @@ with its number and store it in BN1

            BN2 SWAP SUBST EVAL 'BN2' STO   @@ RCL the BN2 und substitute the "C"

                                                            @@ with its number and store it in BN2

                                                            @@ as the prepared BP of J + 1

            NEXT

    »

  ELSE \-> N

    « B0 INTVX 'C' + DUP 'BN1' STO 

      INTVX DUP 'BN2' STO 

      'X=1' SUBST EVAL 0 = 'C' ISOL DUP

      BN1 SWAP SUBST EVAL 'BN1' STO 

      BN2 SWAP SUBST EVAL 'BN2' STO

      IF N 1 > 

      THEN 

          2 N FOR J 

               BN2 J * 'C' + EVAL DUP 

               'BN1' STO INTVX EVAL DUP 

               'BN2' STO 'X=1' SUBST EVAL 0 = 'C' ISOL DUP 

               BN1 SWAP SUBST EVAL FDISTRIB 

               'BN1' STO 

               BN2 SWAP SUBST EVAL 

               'BN2' STO

        NEXT

      END

    »

  END

»

Enjoy it and tell me your improvements and critics.

SORRY SORRY SORRY, dear Mr. Admin move this thread to "General Software Libary".

greetings
peacecalc