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let be the integral:

[tex]\int_0^{\infty}F(x)dx [/tex] with [tex]x\rightarrow\infty F(x)\rightarrow0 [/tex] then we make the change of variable x=-e^{t} then the new integral would become [tex]\int_{-\infty}^{\infty+i\pi}F(-e^t)e^{t}dt[/tex] my question is if we can ignore the integral from [tex] (\infty,\infty+i\pi) [/tex] so we have only the integral [tex]\int_{-\infty}^{\infty}F(-e^t)e^{t}dt [/tex] as for big value the F(x) tends to 0

[tex]\int_0^{\infty}F(x)dx [/tex] with [tex]x\rightarrow\infty F(x)\rightarrow0 [/tex] then we make the change of variable x=-e^{t} then the new integral would become [tex]\int_{-\infty}^{\infty+i\pi}F(-e^t)e^{t}dt[/tex] my question is if we can ignore the integral from [tex] (\infty,\infty+i\pi) [/tex] so we have only the integral [tex]\int_{-\infty}^{\infty}F(-e^t)e^{t}dt [/tex] as for big value the F(x) tends to 0

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