# How to evaluate sums that have 0^0 = 1

In my code:

summand[k_, x_] := (0.25*x*mu)^k/(k!*Pochhammer[(m + 1)/2, k])*
Hypergeometric1F1[(m + 1)/2, (m + 1)/2 + k, eta];

cumdistfunc[x_] := 1 - 0.5^(m (m + 1)) Exp[-eta] Exp[Tr[kappa x]] Sum[summand[k, x], {k, 0, 20}]


I have that the summand function ought to be able to be evaluated at 0 so that the value of my cumulative distribution function at 0 is actually 0. Do you know how I could do that?

Thank you so much!

• Ok, the typesetting from Mathematica did not work but here is the dilemma: The sum at k=0 will involve 0^0 for x=0. This is an analytic result that is a cumulative distribution function which should evaluate to zero at x=0 and then be gradually increasing. – Hirek Sep 1 '14 at 16:32
• Have you tried defining the special case cumdistfunc[0]=0 before your first line of code? – Hector Sep 1 '14 at 19:12
• I will do that; it sounds reasonable. However, is there a feature in Mathematica that lets you evaluate an infinite sum in a truncated fashion? Technically the sum should be infinite. Thank you so much! – Hirek Sep 2 '14 at 11:06