Error in implemented function

Hello,

I have the function written above. It was calculated by WolframAlpha and the result is 0.

I've tried to implement the formula in Matlab with the code below:

 tmp=0;
for s=0:24
    if (48-s >= 24)
        bin1 = nchoosek(48-s,24);
    else
        bin1 = 0;
    end

    if (47-s >= 24)
        bin2 = nchoosek(47-s,24);
    else
        bin2 = 0;
    end

    tmp = tmp + (-1)^s * nchoosek(24,s) * (bin1-bin2);  
end

But my code outputs (variable tmp) the result -2 instead of 0. I am not seeing, where the mistake is.

I would appreciate, if someone could help me.

Answer 1

[Michal]

The double precision (default numerical values class in Matlab) is not enough for this kind of computation!!! You need to use symbolic math toolbox, to get multi-precision accuracy. Wolfram alpha (with Mathematica engine) using this approach by default.

Just a simple code using matlab symbolic toolbox: tmp = 0 !!!

tmp=sym(0);
syms s
for s=0:24
    bin1 = nchoosek(sym(48)-s,sym(24));
    bin2 = nchoosek(sym(47)-s,sym(24));
    aux = (-1)^s * nchoosek(sym(24),s) * (bin1-bin2);
    tmp = tmp + aux;
end
tmp

But you must know, that symbolic computations are significantly slower than numerical computations (double class).

[Stephen23]

+1 nice explanation.

[Nik joung]

Thank you, for your nice explanation! It helps me a lot to get behind such problems.

And if I want to do further calculations with the result, I just use the double()-function on the resulting sym-variable.