MATLAB: Anonymous function to calculate a sum

anonymous function

Hye

I have to write an anonymous function which calculates the following sum for a given real number x and a positive integer:

x + (x^2)/2! + (x^4)/4! + … + (x^2n)/(2n)!

I started off with this:

ch = @(x,n) …

But I don't know how I can calculate the sum with only the anonymous function.

>> fun = @(x,n) x + sum(x.^(2:2:2*n) ./ factorial(2:2:2*n));
>> fun(3,5)
ans =  12.066

Compare against your expansion:

>> x = 3;
>> fun(x,2)
ans =  10.875
>> x + (x^2)/factorial(2) + (x^4)/factorial(4)
ans =  10.875

fun3 = @(x) fun1(x) + fun2(x)

On each loop iteration the flag value changes sign, so it follows this pattern:

+1
-1
+1
-1
...

This has the effect of alternately adding or subtracting the following term:

+ (x^0)/factorial(0)
- (x^2)/factorial(2)
+ (x^4)/factorial(4)
- (x^6)/factorial(6)
...

This avoids the need to call two different plus and minus operators (but that would also be a perfectly viable approach).