.Alternate to using for loop or symsum for the summation ∑(const)^n/(n*n!) ?

Dear all,

Is there a more computationally efficient way compared to using for loop or symsum (from Symbolic math toolbox) to compute:

∑(const)^n/(n*n!)

const is some constant value, n is the range of limit varying from 1 to infinity (or some high value like 200 for approximating the sum).

-- Thanks, Ram.

[Sean de Wolski]

Why not symsum? You're going to need it for factorial greater than 170 anyway:

factorial(171)

[Ramaprasad Kulkarni]

I am using symsum and it is computationally expensive. It takes a lot of time (like half an hour for my program). I am not using 'for loop' anymore which I assume would have been worse computationally.

Answer 1

[Roger Stafford]

Your sum is equal to the integral

 int('(exp(x)-1)/x','x',0,const)

so you could do numerical integration of this rather than summing the infinite series. That integrand is actually well-behaved in the vicinity of x = 0, but computing it might give you some problems, so you could substitute a Taylor series approximation very near x = 0.

[Ramaprasad Kulkarni]

Well, I used symsum with 'range 1 to 200' which runs much faster without much difference in results compared to the 'range 1 to infinity' (which I was using earlier).

-- Thanks for your replies.