The following expression shows up a lot in optics: U(r, z) = eikv=+r² _ pikz (4) Expand it to second order in r. You can assume that r « z and kz > 1. Expanding to second order in r means "Write down...

Extracted text: The following expression shows up a lot in optics: U(r, z) = eikv=+r² _ pikz (4) Expand it to second order in r. You can assume that r « z and kz > 1. Expanding to second order in r means "Write down a Taylor series that might have terms independent of r, might have terms linear in r, and might have terms proportional to r2, but won't have any terms with r3 or higher powers." It is entirely possible that some of those terms will be absent (or, if you prefer, will have coefficient zero), but at least one of them will be present (or, if you prefer, will have a non-zero coefficient).