# Analytical expressions for inescapable exponential producing capabilities Answer

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Analytical expressions for inescapable exponential producing capabilities

I’m
$$f_{j,okay}(x) = sum_{n=0}^infty frac{x^n}{(okay+jcdot n)!}$$
the place $$j$$ is a optimistic integer, and $$okay = 0,ldots, j-1$$. The illustration $$j = 1$$ admits the expression
$$f_{1,okay}(x) = e^x x^{-k} frac{Gamma(okay) – Gamma(okay,x)}{Gamma(okay)}$$
by way of respectively the Gamma duty and the unfinished Gamma duty. The downside emerges within the resolution of stationary p.d.f. of unostentatious chemical response networks Markov dynamics. I can participate extra insights on this if of ameliorate.

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