Bailey mod 9 Identities

Author

Eric W. Weisstein
March 11, 2005

This notebook downloaded from http://mathworld.wolfram.com/notebooks/SpecialFunctions/BaileyMod9Identities.nb.

For more information, see Eric's MathWorld entry http://mathworld.wolfram.com/BaileyMod9Identities.html.

©2005 Wolfram Research, Inc. except for portions noted otherwise

Additional Authors

Contributed by
Andrew Sills
Rutgers University
March 8, 2005

Identities

A(q)=(∑_(n=0)^∞)((Subscript[(q^(3(n^2)))(q;q), 3n])/((Subscript[((q^3);(q^3)), n])(Subscript[((q^3);(q^3)), 2n])))=((Subscript[((q^4),(q^5),(q^9);(q^9)), ∞])/(Subscript[((q^3);(q^3)), ∞]))

Series[Sum[(((q^(3(n^2)))QSeries[{q,q},3n])/(QSeries[{(q^3),(q^3)},n]QSeries[{(q^3),(q^3)},2n])),{n,0,20}],{q,0,20}]

Series[((QSeries[{{(q^4),(q^5),(q^9)},(q^9)}])/(QSeries[{(q^3),(q^3)}])),{q,0,20}]

CoefficientList[%,q]

B(q)=(∑_(n=0)^∞)(((Subscript[(q^(3(n^2)+3n))(q;q), 3n])(1-(q^(3n+2))))/((Subscript[((q^3);(q^3)), n])(Subscript[((q^3);(q^3)), 2n+1])))=((Subscript[((q^2),(q^7),(q^9);(q^9)), ∞])/(Subscript[((q^3);(q^3)), ∞]))

Series[Sum[(((q^(3(n^2)+3n))QSeries[{q,q},3n] (1-(q^(3n+2))))/(QSeries[{(q^3),(q^3)},n]QSeries[{(q^3),(q^3)},2n+1])),{n,0,20}],{q,0,20}]

Series[((QSeries[{{(q^2),(q^7),(q^9)},(q^9)}])/(QSeries[{(q^3),(q^3)}])),{q,0,20}]

CoefficientList[%,q]

C(q)=(∑_(n=0)^∞)((Subscript[(q^(3(n^2)+3n))(q;q), 3n+1])/((Subscript[((q^3);(q^3)), n])(Subscript[((q^3);(q^3)), 2n+1])))=((Subscript[(q,(q^8),(q^9);(q^9)), ∞])/(Subscript[((q^3);(q^3)), ∞]))

Series[Sum[(((q^(3(n^2)+3n))QSeries[{q,q},3n+1])/(QSeries[{(q^3),(q^3)},n]QSeries[{(q^3),(q^3)},2n+1])),{n,0,20}],{q,0,20}]

Series[((QSeries[{{q,(q^8),(q^9)},(q^9)}])/(QSeries[{(q^3),(q^3)}])),{q,0,20}]

CoefficientList[%,q]