How to make and plot a function with a summation?

Goodevening everybody,

I've been trying to make and plot the following function in Matlab:

I have the values for ak in a vector (n is max 100). I've been trying with symsum function and for loops in a sorts of ways but can't get it to work.

I hope someone can help me :)

Answer 1

[Birdman]

Try this:

n=100;
a=sym('a',[n+1 1]);
syms x k
SmbSum=symsum(a(k+1)*x^k,k,0,n);

[Bas Helfrich]

Getting the following error:

Error using sym/subsindex (line 796) Invalid indexing or function definition. When defining a function, ensure that the arguments are symbolic variables and the body of the function is a SYM expression. When indexing, the input must be numeric, logical, or ':'.

For some reason it doesn't take the values out of the vector.

[Birdman]

Try the following approach:

n=100;
a=sym('a',[n 1]);
syms x k
eq=sym(zeros(n,1));
for i=1:n
    eq(i)=a(i)*x^i;
end
eq=sum(eq)

[Bas Helfrich]

This seems to work, only put in the numers and it should work. Thanks for your help!

[Birdman]

You are welcome. If it helped, can you accept it?

[Bas Helfrich]

I am able to put in the a values, but not yet the x to be able to make a plot of the function.

[Birdman]

To replace a value with a symbolic variable, use subs command. For instance

x=subs(x,1);

or

x=subs(x,0:0.1:1);

[Bas Helfrich]

And it works, thanks a lot!

Answer 2

[Steven Lord]

Do you want this to be a symbolic expression with x as the symbolic variable? Or do you have a numeric value for x and want the result of evaluating this polynomial?

In the former case, see the poly2sym function.

In the latter case, I would be very careful about doing anything with a polynomial of degree 99. You're almost begging for catastrophic cancellation. But if you are careful you could use the polyval function.

[Bas Helfrich]

Eventually I want to make a plot with this function with -8 < x < 8. So with numeric values for x. I'll try the polyval function, but I still have to define the function first...

[Steven Lord]

Keep in mind:

>> x = 8^99
x =
   2.5463e+89

You're going to be adding and subtracting extremely large numbers at the edges of your ranges if you go up to a degree 99 polynomial. See the catastrophic cancellation link I included in my response.

If your polynomial is of modest degree, you already have the polynomial you need to use polyval. It takes a coefficient vector and you said "I have the values for ak [the coefficients] in a vector".

x = polyval([1 2 3], 4)
y = 1*4^2 + 2*4^1 + 3*4^0
f = @(x) x.^2 + 2*x.^1 + 3;
z = f(4)

Answer 3

[Torsten]

Is this the partial Taylor series of a certain function f ?

In this case, you could use

f=...;
n=...;
fn = taylor(f,x,'order',n);
fplot(fn);
xlim([-4 4])
grid on

Best wishes

Torsten.