code a series using matlab that involve Pochhamer sumbol

Question

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I am trying to model the following series using matlab code but I dont know how to approach it

$\sum_{i=1}^n \frac {n!} {(n-i)!(\lambda- \mu)(\lambda-2 \mu)....(\lambda- i\mu)}$

I know that

is a Pochhamer sumbol. I want to be able to represent the following series in Matalb using vectorization

In particular, the above series can be coded in MATLAB as:

i = 1:n;

y =factorial(n)./(factorial(n-k).*prod(1./(lam-u.*(1:k))));

result=sum(y);

but this doesnt work. Any suggestions?

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Answer 1

David Hill 2022-3-3

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If lam and u are not going to change, you could compute the series for the largest n as follows:

for m=1:18
  p(m)=prod(lam-(1:m)*u);
end

Then the rest can be vectorized.

y=sum(factorial(n)./factorial(n-(1:n))./p(1:n);