.Alternate to using for loop or symsum for the summation ∑(const)^n/(n*n!) ?
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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.
2 Comments
Sean de Wolski
on 26 Jun 2013
Edited: Sean de Wolski
on 26 Jun 2013
Why not symsum? You're going to need it for factorial greater than 170 anyway:
factorial(171)
Accepted Answer
Roger Stafford
on 26 Jun 2013
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.
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