The definition of the adjective expectant is having or marked by expectation, where expectation is a feeling of eagerness or anticipation. For example, if you say you’re going to give your daughter a piece of cake in five minutes, she might be rather expectant until then.
Expectant is also a euphemism for pregnant or expecting a baby. It usually precedes the noun it modifies (e.g., expectant mother or expectant parents), while expecting is usually used in pregnancy-related contexts where a predicate adjective is called for (e.g., She feels sick this morning because she is expecting).
Where expectant could be replaced with expected or expecting, it usually makes sense to do so. Expectant connotes eagerness or anticipation, while expected and expecting tend to be more neutral.
In these instances, expectant is a euphemism for pregnant or means marked by expectation:
[T]he results should provide great confidence for expectant mothers who suffer from epilepsy or any of the other disorders. [Los Angeles Times]
[S]and there long enough, looking expectant, and someone on the other side of the case will eventually take a break from frantically making sandwiches to take an order. [AV Club]
The mood was breathless and expectant, like the close of the first movement of Ravel’s Piano Concerto extended for an entire movement. [Sydney Morning Herald]
And these writers use expectant where expecting or expected might work better:
The children’s apprenticeship is actually very important to the future of patients because of an expectant [expected?] shortage of medical professionals. [7 Online]
Her temporary permission expires in April next year but she has applied already and is expectant of being given [is expecting to be given?] another one before then. [Total Essex]
The police are expectant [expecting?] to also find militants amongst the illegal immigrants … [Daily Times]