Specialist Wizards

From Darfuria

Specialist wizards gain levels from their XP using the same table as illusionists in the PHB.

Specialist wizards, including illusionists, also gain spells as specified in the table for illusionist spells castable per illusionist level, at +1 bonus spell per level. This is because specialist wizards can learn one extra spell from their chosen school of specialisation per level. Assuming at least one spell will be from their specialised school, then the illusionist table +1/spell level seems to be logical.

Please refer to the tables on p. 26 of the PHB.