I am interested in R functions for the following integrals / sums (expressed best I can in text)  -

Normal: G_u(k) =  Integration_{Lower limit=k}^{Upper limit=infinity} [(u -k) f(u) d(u)], where where u is N(0,1), and f(u) is the density function.

Poisson: G(lambda,k) = Sum_{Lower limit=k}^{Upper limit=infinity} [(x-k) p(x, lambda)] where P(x,lambda) is the Poisson prob function with parameter lambda.

The Normal expression is very commonly used in inventory management to determine safety stocks (and its tabular values can be found in some texts) - and I am also looking for Poisson and/or Gamma as that'd fit the situation better. 

I am wondering if there are standard functions in R that might allow me to get these values, instead of needing to do the numerical integration, etc. myself.
                                                    Thank you very much.

  
 
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