In 1936, Watson found that under the action of elements of the modular group, the order 3 mock theta functions almost transform like modular forms of weight  (multiplied by suitable powers of q), except that there are "error terms" in the functional equations, usually given as explicit integrals.
In 1936, Watson discovered that under the influence of elements from the modular group, the order 3 mock theta functions behave almost like modular forms with a weight (multiplied by suitable powers of q), but they have "error terms" in their functional equations, typically presented as explicit integrals.