Passage: The series 1 − 2 + 3 − 4 + ... is closely related to Grandi's series 1 − 1 + 1 − 1 + .... Euler treated these two as special cases of 1 − 2n + 3n − 4n + ... for arbitrary n, a line of research extending his work on the Basel problem and leading towards the functional equations of what are now known as the Dirichlet eta function and the Riemann zeta function.

Question: what are the two functions that came from work on the Basel problem?
the Dirichlet eta function and the Riemann zeta function