gamma function error in calculation

% Starting value

The above formula is coded as follows:

syms x a
Y=sym(zeros(1));
Y(1)=0;
a=1/2
for i=1:4
    if i==5
        A=1
    else
        A=0
    end
    if i==4
        B=1
    else
        B=0
    end
    Y(i+1)=simplify((gamma(a*(i-1)+1)/gamma((a*(i-1)+3/2))*(A-Y(i)+((2*B)/gamma(5/2)))));
end
disp(Y)

But it is showing the calculation error Y(5)=1 but the value is shown in MATLAB is as follows:('2535301200456458897054207582575/2535301200456458802993406410752'). Ecxept Y(5) all values are zeros

Answer 1

[VBBV]

syms x a
Y=sym(zeros(1));
Y(1)=0;
a=1/2

a = 0.5000

for i=1:4
    if i==5
        A=1;
        B = 0;
         Y(i+1)=simplify((gamma(a*(i-1)+1)/gamma((a*(i-1)+3/2))*(A-Y(i)+((2*B)/gamma(5/2)))));
    else
        A=0;
        B =1 ;
         Y(i+1)=simplify((gamma(a*(i-1)+1)/gamma((a*(i-1)+3/2))*(A-Y(i)+((2*B)/gamma(5/2)))));
    end
    if i==4
        B=1;
        A = 0;
         Y(i+1)=simplify((gamma(a*(i-1)+1)/gamma((a*(i-1)+3/2))*(A-Y(i)+((2*B)/gamma(5/2)))));
    else
        B=0;
        A = 1;
         Y(i+1)=simplify((gamma(a*(i-1)+1)/gamma((a*(i-1)+3/2))*(A-Y(i)+((2*B)/gamma(5/2)))));
    end
   
end

A = 0

B = 0

A = 1

A = 0

B = 0

A = 1

A = 0

B = 0

A = 1

A = 0

B = 1

disp(vpa(Y,4))

[VBBV]

For each if condition , there are few unknown variables e.g. either A or B in the equation.

So, to compute whole equaton for each iteration, values have to be defined with A and B or computed to get final matrix Y.

[yogeshwari patel]

The correct value are Y(1)=0; Y(2)=0;Y(3)=0, Y(4)=0, Y(5)=1 and rest value s are zero. Now if I work with pen and paper the values are same as I mention above but when I work with MATLAB code the value of Y(5)=2535301200456458897054207582575/2535301200456458802993406410752 .Why that error is appaering

[Torsten]

You mix symbolic and floating point parameters in the calculation of Y(5). This will result in reduced accuracy.