considering the flowing code:
————————————————————————
from sage.symbolic.assumptions import GenericDeclaration;
var('lamda,n,k,p');
decl1 = GenericDeclaration(k, 'integer');
decl1.assume();
assume(k>0,k>1,n>k,lamda>0,lamda<n);
ep=binomial(n,k)*p^k*(1-p)^(n-k);
ep=ep.subs_expr(p==lamda/n);
ep=ep.subs_expr(binomial(n,k)==factorial(n)/factorial(k)/factorial(n-k));
ep=limit(ep,n=oo);
ep.simplify_full();
————————————————————————
the result is:
lamda^k*limit((-(lamda - n)/n)^n*factorial(n)/((-lamda +
n)^k*factorial(-k + n)), n, +Infinity)/factorial(k)
————————————————————————
it is not the simplest form.
In fact , sage will give me the simplest form as below when I paste the
result above to sage again.
————————————————————————
lamda^k*e^(-lamda)/factorial(k)
————————————————————————
the question is how can i get the simplest form directly?
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