Analytical continuation...

Let,s suppose we have the asymptotyc development of the integral:

$$\int_{x}^{\infty}F(t)=g(x)[1+a/x+b/x^{2}+c/x^{3}+....]$$

where a,b,c,.. are known constants and g(x) is a known function then you all will agree that this expression could be useful to compute the integral when x-------->oo, my question is if this expression can be analytically continued to calculate the integral for low x for example x=1,2,3.......

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 Recognitions: Homework Help Science Advisor Why would I want to compute the integral $$\int_{x}^{\infty}F(t)dt$$ as x tends to infinity? If that integral exists for all x, then obviously I know that the limit, as x tends to infinity must be zero without doing any computation.
 yes but perhaps you are interested in knowing the values of the integral for big x x=100,1000,100000000000000 or for low x x=1,2,3,4,.....

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