Rogers mod 14 Identities

Author

Eric W. Weisstein
December 22, 2008

This notebook downloaded from http://mathworld.wolfram.com/notebooks/SpecialFunctions/RogersMod14Identities.nb.

For more information, see Eric's MathWorld entry http://mathworld.wolfram.com/RogersMod14Identities.html.

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

Undocumented listability

QPochhammer[{q,q^2},q,n]

Identities

A(q)=(∑_(n=0)^∞)((q^(n^2))/((Subscript[(q;q), n])(Subscript[(q;(q^2)), n])))=((Subscript[((q^6),(q^8),(q^14);(q^14)), ∞])/(Subscript[(q;q), ∞]))

Sum[((q^(n^2))/(QPochhammer[q,q,n]QPochhammer[q,(q^2),n])),{n,0,∞}],

Series[Sum[((q^(n^2))/(QPochhammer[q,q,n]QPochhammer[q,(q^2),n])),{n,0,20}],{q,0,20}]

Series[((Times@@QPochhammer[{(q^6),(q^8),(q^14)},(q^14)])/(QPochhammer[q])),{q,0,20}]

CoefficientList[%,q]

B(q)=(∑_(n=0)^∞)((q^((n^2)+n))/((Subscript[(q;q), n])(Subscript[(q;(q^2)), n+1])))=((Subscript[((q^4),(q^10),(q^14);(q^14)), ∞])/(Subscript[(q;q), ∞]))

Series[Sum[((q^((n^2)+n))/(QPochhammer[q,q,n]QPochhammer[q,(q^2),n+1])),{n,0,20}],{q,0,20}]

Series[((Times@@QPochhammer[{(q^4),(q^10),(q^14)},(q^14)])/(QPochhammer[q])),{q,0,20}]

CoefficientList[%,q]

C(q)=(∑_(n=0)^∞)((q^((n^2)+2n))/((Subscript[(q;q), n])(Subscript[(q;(q^2)), n+1])))=((Subscript[((q^2),(q^12),(q^14);(q^14)), ∞])/(Subscript[(q;q), ∞]))

Series[Sum[((q^((n^2)+2n))/(QPochhammer[q,q,n]QPochhammer[q,(q^2),n+1])),{n,0,20}],{q,0,20}]

Series[((Times@@QPochhammer[{(q^2),(q^12),(q^14)},(q^14)])/(QPochhammer[q])),{q,0,20}]

CoefficientList[%,q]