error in logical calculation

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)
%%%%%%%%%%%%%%%%%%%%%

for i=4 ,the value of Y(5) should be 1 but it is showwing s2535301200456458897054207582575/2535301200456458802993406410752. If i work with pen and paper and simplify it again i get 1 .So what is the mistake in the code

    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%    Question -2 
    syms x a
    series(x)=sym(zeros(1));
    Y=sym(zeros(1));
    m=sym(1);
    Y(1)=0;
    Y(2)=a;
    %N=input ('enter the number of coefficient required')
    for k=1:6          
        Y(k+2)=((18*kroneckerDelta(k,m)-9*Y(k)))/(k*(k+1));
    end
    disp(Y)
    for  k=1:6
        series(x)=series(x)+Y(k)*(power(x,k-1));
    end
    series % Find the series in terms of a and x 
    M=series(pi/2)-1
    a=solve(M) % find the value of a 
    series

I want to put the value of a in series and want to evaluete the series in terms of x only. I used the command series but it is not working

[SL: edited to pull the prose in the middle of the two questions out of the code block.]

[Jan]

Please explain "is not working" with any details. It is easier to solve a problem than to guess, what the problem is.

Answer 1

[Yash]

Hi Yogeshwari,

I understand that you have two queries:

1. The value of 'Y(5)' is not 1 through your code.
2. You are interested in substituting the value of a in series and want to get series in terms of a.

For the first query, upon observation, I have found out that the value you have obtained is very close to 1. When pasting the same value in the MATLAB command window, it evaluates to 1. To obtain the desired result, you can use the "eval" function to evaluate the expression. You just need to make one change in your code as follows:

Y(i+1)=eval((gamma(a*(i-1)+1)/gamma((a*(i-1)+3/2))*(A-Y(i)+((2*B)/gamma(5/2)))));

You can refer to the MATLAB documentation of the "eval" function in the following link:

https://www.mathworks.com/help/matlab/ref/eval.html

Regarding the second query, I suggest you to first change the name of the variable which stores the value of 'a' after solving 'M'. This will help to avoid confusion between the symbolic variable 'a' and the variable 'a' used in your code.

To substitute the value of 'a', you can use the "subs" function as shown below:

aval=solve(M) % find the value of a 
series(x) = subs(series(x),a,aval)

The MATLAB documentation of the "subs" function is available at the below link:

https://www.mathworks.com/help/symbolic/subs.html

You can further use the "eval" function if the expressions are complex. If the values involve large fractions, you can use the "vpa" function to apply variable-precision arithmetic.

Refer to the below link to get more details of the "vpa" function:

https://www.mathworks.com/help/symbolic/vpa.html

I hope this addresses your query.

Best Regards

Yash

[Stephen23]

Note that EVAL is not actually a function defined for the symbolic toolbox:

https://www.mathworks.com/help/symbolic/referencelist.html?type=function