q-Beta Function

Author

Eric W. Weisstein
March 28, 2006

This notebook downloaded from http://mathworld.wolfram.com/notebooks/SpecialFunctions/q-BetaFunction.nb.

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

©2006 Wolfram Research, Inc. except for portions noted otherwise

Definition

Regular Beta Function

Integrate[(t^(a-1))(((1-t))^(q-1)),{t,0,1}]

q-Beta Function

Integrate[(t^(b-1))QPochhammer[q t,q,a-1],{t,0,1}]

Table[Integrate[(t^(b-1))Product[(1-q t q^n),{n,0,a-1}],{t,0,1},Assumptions->Re[b]>0],{a,2}]//Simplify