infinite series with loop in MATLAB

how can find F in matlab , where the initial value of z =1

and i is loop from

i=1:10

thanks so much for any help.need code of program if possible

[David Hill]

It is unclear what z array is (from i=1:10) and how i changes in the equation. Should there be another summation on the outside changing i from 1:10?

[hasan s]

thank you for your reply

yes .to chang z

there must summation for i=1:10 ,with initial value to z=1

and another summation k=1:infinity .....for series

Answer 1

[Walter Roberson]

syms z I k real
F = symsum((-z*I)^k/(k*factorial(k)), k, 1, inf)

F = 

However, examine the behavior when k = 0, the lower bound from the equation. The denominator is k*k! which would be 0 * 0! which would be 0*1 which would be 0. So we have a potential problem with singularities, and need to look at the limit. For non-zero z and i, (-z*i)^0 would be 1. Thus we are looking at 1/0 and that is infinite. As that is a term that is included in the actual sum (k = 0 to infinity) we must conclude that F is infinite except for the case where z or i are 0.

[hasan s]

thanks for reply

I want loop to evaluate or change z(i) , by using "for i=1:10 ....end" ,with initial value z=1

and summation k=1:infinity .....for series.

is that possible in matlab???

[Walter Roberson]

syms z I k real
F = symsum((-z*I)^k/(k*factorial(k)), k, 1, inf)

F = 

Fsum = sym(0);
for i = 1 : 10
  Fsum = Fsum + subs(F, I, i);
end
Fsum1 = subs(Fsum, z, 1)

Fsum1 = 

vpa(Fsum1)

ans = 

fplot(Fsum, [1 10])

Fvals = zeros(10,1,'sym');
for i = 1 : 10
    Fvals(i) = symsum((-z*i)^k/(k*factorial(k)), k, 1, inf);
end
fplot(Fvals(1:3), [1 10]); legend({'i=1', 'i=2', 'i=3'})

[hasan s]

thanks a lot

but in my question z(i) , not z*i

Do I just change it and the program remains correct???

[Walter Roberson]

No, your question is z*i not z subscript i.

• Your equation has subscripted k=0 on the summation, so if subscripting was intended on the z then it could have been done
• Your equation has k(k!) and there is no way you could possibly index scalar k at location factorial(k) . Therefore in your equation A(B) indicates A multiplied by B.

[Walter Roberson]

syms k real
Z = sym('z', [1 10]);
assume(Z, 'real')
Z(1) = 1;
F = sym(0);
for i = 1 : 10
    F = F + symsum((-Z(i))^k/(k*factorial(k)), k, 1, inf);
end
F

F = 

If the z values are fixed, the way that is fixed, then this would be a scalar outcome that you would not be able to plot.

[hasan s]

thank you very much for all your reply

yes I need the last program when the values of z are fixed numbers.I need the output of this series to be Known value

when I run the last program the output is

F =

- z2*hypergeom([1, 1], [2, 2], -z2) - z3*hypergeom([1, 1], [2, 2], -z3) - z4*hypergeom([1, 1], [2, 2], -z4) - z5*hypergeom([1, 1], [2, 2], -z5) - z6*hypergeom([1, 1], [2, 2], -z6) - z7*hypergeom([1, 1], [2, 2], -z7) - z8*hypergeom([1, 1], [2, 2], -z8) - z9*hypergeom([1, 1], [2, 2], -z9) - z10*hypergeom([1, 1], [2, 2], -z10) - hypergeom([1, 1], [2, 2], -1)

if possible ...

what is meaning "hypergeom "

[Walter Roberson]

Replace

Z = sym('z', [1 10]);
assume(Z, 'real')
Z(1) = 1;

with assigning specific values to Z(1:10)

hypergeom is described at https://www.mathworks.com/help/symbolic/hypergeom.html#bt1nkmw-2 . It is a standardized infinite series rather than a closed form solution in itself. MATLAB knows how to reason about the standardized function, such as knowing how to take a derivative.

syms z
f = hypergeom([1, 1], [2, 2], -z)

f = 

diff(f,z)

ans = 

Standardized infinite series are common in mathematics; for example sin(x) is a standardized infinite series.

[hasan s]

Is it possible to add a condition to the program so that the output does not contain hypergeom???

I need the output are real values

[Walter Roberson]

As usual, you can double() the result, provided that all of the z have been given specific numeric values.

[hasan s]

ok I will give z specific numeric values. but excuse me, if possible , what mean double() the result?? what I change in program??

[Walter Roberson]

format long g
z = [1, rand(1,9)];

syms k real
F = sym(0);
for i = 1 : 10
    F = F + symsum((-z(i))^k/(k*factorial(k)), k, 1, inf);
end
F

F = 

result = double(F)

result = 
         -4.34857820351754

[hasan s]

Thank you very much