Question: What mean GAMMA(N+1,1)??

Hi all,

> a := k -> 2/factorial(k);

                                          2      
                           a := k -> ------------
                                     factorial(k)
> Sn := n -> sum(a(k), k = 1 .. n);

                                         n       
                                       -----     
                                        \        
                                         )       
                            Sn := n ->  /    a(k)
                                       -----     
                                       k = 1     
> Sn(N);

                 -2 GAMMA(N + 1) + 2 exp(1) GAMMA(N + 1, 1)
                 ------------------------------------------
                                GAMMA(N + 1)               

is it true that for large N, Gamma(N+1) approx GAMMA(N+1,1)?

since

> GAMMA(100+1.0) = GAMMA(100+1.0, 1);

                                  157                 157
                    9.332621544 10    = 9.332621544 10   

wich suppose to be because

> sum(a(k), k = 1 .. infinity);

                                2 exp(1) - 2

Mario

P.S.  If someone could put a link to a place where there is a demonstration of that propertie.