Subspace

Author

Eric W. Weisstein
December 24, 2008

This notebook downloaded from http://mathworld.wolfram.com/notebooks/Topology/Subspace.nb.

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

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

Sums

(Subscript[c, e])==(((∑_(k=-∞)^∞)(q^(-(k^2))))/((∏_j^∞)(1-(q^(-j)))))==((EllipticTheta[3, 0, (1/q)])/(QPochhammer2[(1/q), (1/q)]))

((Sum[(q^(-(k^2))),{k,-∞,∞}])/(Product[1-(q^(-j)),{j,∞}]))//FullSimplify

FunctionExpand[%]//FullSimplify

(Subscript[c, o])==(((∑_(k=-∞)^∞)(q^(-(((k+(1/2)))^2))))/((∏_(j=1)^∞)(1-(q^(-j)))))==((EllipticTheta[2, 0, (1/q)])/(QPochhammer2[(1/q), (1/q)]))

((Sum[(q^(-(((k+1/2))^2))),{k,-∞,∞}])/(Product[1-(q^(-j)),{j,∞}]))

Sum[(q^(-(((k+1/2))^2))),{k,-∞,∞}]

V6

Sum[(q^(((k+1/2))^2)),{k,-∞,∞}]

Sum[(q^(-(((k+1/2))^2))),{k,-∞,∞}]

Simplify[%,q>0]

$Version

V7

Sum[(q^(((k+1/2))^2)),{k,-∞,∞}]

Sum[(q^(-(((k+1/2))^2))),{k,-∞,∞}]

$Version