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Reference.org
Euler function
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<p>In <a href="/facts/Mathematics/pxTouaz4">mathematics</a>, the Euler function is given by </p> ϕ ( q ) = ∏ k = 1 ∞ ( 1 − q k ) , | q | < 1. {\displaystyle \phi (q)=\prod _{k=1}^{\infty }(1-q^{k}),\quad |q|<1.} <p>Named after <a href="/facts/Leonhard_Euler/z2fsbjgj">Leonhard Euler</a>, it is a model example of a <a href="/facts/Q-series/keASLfpe"><i>q</i>-series</a> and provides the prototypical example of a relation between <a href="/facts/Combinatorics/k14xUoKT">combinatorics</a> and <a href="/facts/Complex_analysis/hgCoQlH0">complex analysis</a>. </p>