(50g) Bernoulli polynomials

[peacecalc]

Hello Keith,

of course here is the code:

Code:



« \-> M X '\GS(N=0,M,1/(N+1)*\GS(K=0,N,(-1)^K*COMB(N,K)*(X+K)^M))'
»

That is ttw's expression: when I input 11 and 'X', at the machine forced me to switch to approximative mode (If I refuse to switch in approximative mode, the program interrupts and ends...) I get after some minutes:

Code:


'X^11.+-5.5*X^10.+9.1666666666*X^9.+0.*X^8.+-11.*X^7.+-.00000002*X^6.+10.99999999*X^5.+-.000003*X^4.+-5.500011*X^3.+-.416696676667*X^2.+.416646633333*X-.41678'

Most of the constants in front of the powers of X are approx. correct, but not the last one: .41678, that one have to be 0 or near by, because every Bernoulli number with odd n greater or equal 3 is zero. And the approximative numbers of X^4 or X^6 are drifting away from zero (it should be like the zero by X^8)

My program working with the integral returns:

Code:


'X^11-11*X^10/2+55*X^9/6-11*X^7+11*X^5-11*X^3/2+5*X/6'

The coeffcients are exact, because the machine works in exact mode.
So what is the problem: the summation function \GS or the combination function COMB?

After some work on the programs workig with summations the PSI function dont't appear any longer, but don't ask me why.

greetings
peacecalc