In order to calculate the left hand side (LHS) you'll want to determine when the nth term is small enough to neglect. The following code employs a user defined tolerance to specify when to terminate the summation (while loop). Not knowing what m, gamma and lambda are I just put in a random tolerance. You'll have to decide upon that yourself. With this code you will be able to subtract the right hand side (RHS) from the LHS and then optimize around lambda using fminsearch (or the like).
LHS = 0;
nth_Term = 0;
Tol = 0.001;
k = 0;
while nth_Term > Tol
nth_Term = (lambda*gamma/2)^k/(factorial(k)*(m+k)^0.5);
LHS = LHS + nth_Term;
k = k+1;
end
I just noticed you put in values for gamma and m, because of the size of gamma lambda had better be a fraction or this function will blow up. That knowledge will help to refine your optimization function.
