Euler's function

In mathematics, the Euler function is given by

Named after Leonhard Euler, it is a model example of a q-series, a modular form, and provides the prototypical example of a relation between combinatorics and complex analysis.

The coefficient ${\displaystyle p(k)}$ in the formal power series expansion for ${\displaystyle 1/\phi (q)}$ gives the number of all partitions of k. That is,

where ${\displaystyle p(k)}$ is the partition function of k.

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