Suppose I have a function

F[r_]:= A/r + B/r^2 + Conjugate[C]/r^3 

with A, B, C being complex numbers and r being a real variable. I would like to series expand


in powers of inverse r. How do I tell mathematica to treat A, B, and C as complex numbers while r as a real variable? Can I do this when defining the function F[r]? Can I do this while using Series[] ? Which is the shortest way to do this?


1 Answer 1



F[r_]:= A/r + B/r^2 + Conjugate[C]/r^3

here are two ways:

Series[ComplexExpand[Re[F[r]^3], {A, B, C}], {r, ∞, 4}] // FullSimplify
   (A^3 + Conjugate[A]^3)/(2 r^3) + Re[-3 Im[A] (B Im[A] + 2 A Im[B]) +
   3 B Re[A]^2]/r^4 + O[r, ∞]^5

if you only want a few terms, or

Collect[ComplexExpand[Re[F[r]^3], {A, B, C}] /. r -> 1/u, u, FullSimplify] /. u -> 1/r

if you want the full expansion.


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge that you have read and understand our privacy policy and code of conduct.

Not the answer you're looking for? Browse other questions tagged or ask your own question.