2
votes
0answers
135 views

Sum of binomial coefficients weighted by a lower incomplete regularized gamma function

The following summation turned up in the course of my research: $$S_n=\sum_{k=0}^n {n \choose k}\lambda^k P(k,t)$$ where $P(k,t)=\frac{1}{\Gamma(k)}\int_{0}^t e^{-x}x^{k-1}dx$ is the lower ...
0
votes
0answers
81 views

Simplifying a finite difference sum that represents a model posterior to avoid numerical issues.

Problem Is it possible to simplify/rewrite the following expression, preferably without explicit sums, such that it can be computed without numerical issues when the $n_*$ are in the range of ...