Please help me write this summation in MATLAB

I am trying to write this double summation in MATLAB. However, I am not getting the correct. Please help me write this.

Please note that the upper limit in the second summation is the floor function.

[Dyuman Joshi]

What have you tried yet? Please show your code.

[Manotosh Kumbhakar]

Hi Dyuman Joshi, I have now done it using symsum in MATLAB. Earlier I was using for loop. However I observed that there is 'symsum' available in MATLAB, which can easily handle such summation notation. For this case, I have written the code as follows and it's now working well!

syms k x n
n_term=50;
f=symsum(((((-1)^(k-1))*(x)^k)/(factorial(k)*2^(k-1)))*symsum(1/(1+(2*n)),n,0,floor((k-1)/2)),k,1,n_term)

f = 

[Torsten]

@Manotosh Kumbhakar

Why

(-x)^k

?

[Manotosh Kumbhakar]

Sorry. That was a typo. It should be (x^k). I will edit it.

[Walter Roberson]

When I tested the inner symsum early this morning, I found that it gave the wrong results when the upper bound uses floor. I will write this up later today.

[Torsten]

@Walter Roberson

So the floor function cannot be used in symbolic summation ?

[Walter Roberson]

False alarm. I was working on my phone in MATLAB Mobile in the early hours of the morning, and did not notice that in one case I was using 1/(2*k+1) but in another case I was using 1/(2*k-1)

Answer 1

[Walter Roberson]

n_term = 50/2;
syms n N k integer
syms x
inner = symsum(1/(2*k+1), k, 0, floor((n-1)/2))

inner = 

outer = (-1)^(n-1)*x^n/factorial(n)/2^(n-1) * inner

outer = 

outer_even = simplify(subs(outer, n, 2*N))

outer_even = 

outer_odd = simplify(subs(outer, n, 2*N+1))

outer_odd = 

sum_even = symsum(outer_even, N, 1, n_term)

sum_even = 

sum_odd = symsum(outer_odd, N, 1, n_term)

sum_odd = 

result = simplify(sum_even + sum_odd)

result = 

result_unsplit = symsum(outer, n, 1, n_term*2)

result_unsplit = 

Hmmm... the difference between the two is that the split version has one extra term, the x^51 term. I am not going to bother to chase that down.

result_unsplit = symsum(outer, n, 1, inf)

result_unsplit =