Euler Identity

Author

Eric W. Weisstein
August 3, 2008

This notebook downloaded from http://mathworld.wolfram.com/notebooks/Combinatorics/EulerIdentity.nb.

For more information, see Eric's MathWorld entry http://mathworld.wolfram.com/EulerIdentity.html.

©2008 Wolfram Research, Inc. except for portions noted otherwise

Identity

Product[1+(z^k),{k,∞}]

TraditionalForm[%]

Product[(((1-(z^(2k-1))))^(-1)),{k,∞}]

FullSimplify[%]

FullSimplify[((-1+z)/(z QPochhammer[(1/z),(z^2)]))-((-1+z)/(z QPochhammer[(1/z),(z^2)]))]

Series

Series[(1/2) QPochhammer[-1,q],{q,0,10}]

CoefficientList[%,q]

Table[PartitionsQ[n],{n,0,10}]

SeriesCoefficient[(1/2) QPochhammer[-1,q],{q,0,n}]

GeneratingFunction[PartitionsQ[n],n,q]