How to write the following equation in Matlab or Mathematica?

0
votes

I have the following equation: enter image description here

Where N^{optim} and K are my variables and M and S are just constants. I want to do some processing to this function like maximizing it, solving it for some values. So I need to write it in terms of the symbolic variables in Matlab. But I don't know how the summation for the symbolic variables. Any help, recommendation, comment is highly appreciated. If any one knows how to do it in mathematica, or other software that might help as well but I would prefer Matlab and Mathematica.

Thank you.

1
matlabmathwolfram-mathematica
Is S another constant? – andy mcevoy
yes @andy mcevoy S is another constant – OAH

1 Answers

1
votes
In[1]:= Binomial[no - m, m]/Binomial[no, m] Sum[Binomial[s, i] Binomial[m, no]^i
(1 - Binomial[m, no])^(s - i), {i, 0, k}]

Out[1]= -(((1 - Binomial[m, no])^(-1 - k + s)*Binomial[-m + no, m]*(-(((1 -
Binomial[m, no])^(-1))^s*(1 - Binomial[m, no])^k) + ((1-Binomial[m, no])^(-1))^s*
(1 - Binomial[m, no])^k*Binomial[m, no] + Binomial[m, no]^(1 + k)*
Binomial[s, 1 + k]*Hypergeometric2F1[1, 1 + k - s, 2 + k, Binomial[m, no]/
(-1 + Binomial[m, no])]))/Binomial[no, m])

Check that result carefully before you depend on it.