If , using integration by parts we can show that
.
Hence obtain an asymptotic expansion of [tex]Ei(x)[tex] as . Show that if is replaced by , the same asymptotic expansion holds when . (Hint choose a suitable contour of integration from .)
Is the asymptotic expansion of just
?
To show that this is also the asymptotic expansion of where , do I need to prove that the remainder term as ? What contour should I choose to integrate on?