Calculate Exponentials WITHOUT built-in exponent function?

Greetings!

I am new to MATLAB and going in circles trying to logic my way what should be a simple function:

How do I calculate, using a "for" loop, x^k?

My function inputs are ( x, n ); I start with:

% code
ExpValue = 0;
k = 1;
for i = 1:n;
  ExpValue = ExpValue + ?
end

Recall that I must use a Sum for the exponential function... x*1, x*x, x*x*x all the way to squaring x up to n times.

Thanks!

Answer 1

[Roger Stafford]

Trying to compute x^n using only summation is a terrible method. Surely you would be allowed to use multiplication!

   ExpValue = 1;
   for k = 1:n   % (Corrected)
     ExpValue = ExpValue*x;
   end

[Dillan Masellas]

Thanks! So I've successfully implemented this code - not sure how I didn't see the simplicity.

Now, I am trying to simulate e^x using sum(x^k/k!). I can't use the factorial function, so I'm getting around that by using prod(1:k) where k=1 and k=k+1 in the for loop.

However, the number just grows with the iteration rather than converging on exp(x).

Thoughts?

[Roger Stafford]

You should realize that the number of terms needed in that series to get the desired accuracy depends on the size of x. For large values of x you will need to compute a very large number of terms. Eventually when the factorial n in the denominator sufficiently exceeds x^n, you can quit, but not before that. For example, with x = 10 and n = 20, the value of x^20/20! is 41.1, so you're not done yet with that summation.

Actually this series is only practical for small values of x, say smaller than about 4 or 5. For larger values of x you can take advantage of the fact that exp(a+b) = exp(a)*exp(b) and derive the values of exp(x) in terms of exp for smaller arguments. For example, exp(10.1234) = exp(1)^10*exp(0.1234).

[Life is Wonderful]

This doesn't work for fractional case

n = 10.2

n = 10.2000

x = 2.5;
x ^ n

ans = 1.1455e+04

ExpValue = 1;
for k = 1:n   % (Corrected)
    ExpValue = ExpValue*x;
end
ExpValue

ExpValue = 9.5367e+03

[Walter Roberson]

True, but the original poster only needed integral powers as they were developing a series approximation to exp()