 Under Catalan's influence, Cesàro initially referred to the "conventional formulas" for as "absurd equalities", and in 1883 Cesàro expressed a typical view of the time that the formulas were false but still somehow formally useful.Finally, in his 1890 "Sur la multiplication des séries", Cesàro took a modern approach starting from definitions.The series are also studied for non-integer values of "n"; these make up the Dirichlet eta function.