Golygon

Author

Eric W. Weisstein
September 7, 2008

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

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

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

Formulas

Product[(x^k)+1,{k,1,n-1,2}]==(QPochhammer[-x, (x^2), n/2])

Product[1+(x^k),{k,1,n-1,2}]

Table[Product[1+(x^k),{k,1,n-1,2}],{n,5}]

Product[1+(x^(2k-1)),{k,n/2}]

Table[Product[1+(x^(2k-1)),{k,n/2}],{n,5}]

SeriesCoefficient[QPochhammer[-x,(x^2),(n/2)],{x,0,k}]

(∏_(k=1)^(n/2))((x^k)+1)==(1/2)(QPochhammer[-1, x, n/2+1])

Product[1+(x^k),{k,1,n/2}]

SeriesCoefficient[(1/2) QPochhammer[-1,x,1+(n/2)],{x,0,k}]

Product

Table[SeriesCoefficient[QPochhammer[-x,(x^2),(n/2)],{x,0,((n^2)/8)}]SeriesCoefficient[(1/2) QPochhammer[-1,x,1+(n/2)],{x,0,((n(n/2+1))/8)}],{n,8,40,8}]

SeriesCoefficient[QPochhammer[-x,(x^2),(n/2)],{x,0,((n^2)/8)}]SeriesCoefficient[(1/2) QPochhammer[-1,x,1+(n/2)],{x,0,((n(n/2+1))/8)}]/.n->8k

Table[SeriesCoefficient[(1/2) QPochhammer[-1,x,1+4 k],{x,0,k (1+4 k)}] SeriesCoefficient[QPochhammer[-x,(x^2),4 k],{x,0,8 (k^2)}],{k,0,10}]

Series[QPochhammer[q],{q,0,10}]

SeriesCoefficient[QPochhammer[q],{q,0,n}]