New in Wolfram Mathematica 7: New Categories of Special Functions ◄ previous | next ►
Define q-Legendre Polynomials
Define q-Legendre polynomials a special cases from QHypergeometricPFQ.
In[1]:=

Click for copyable input
QLegendreP[n_Integer?NonNegative, x_, q_] := 

  QHypergeometricPFQ[{q^-n, q^(n + 1), q^(1/4) (x + I Sqrt[1 - x^2]), 

    q^(1/4) (x - I Sqrt[1 - x^2])}, {q, -q, -q^(1/2)}, q, q];
In[2]:=

Click for copyable input
Text@TraditionalForm@

  Grid[Table[{HoldForm[QLegendreP][n, x, q], 

     Collect[Expand[QLegendreP[n, x, q] // FunctionExpand, x], x, 

      Simplify]}, {n, 0, 5}], 

   Background -> {None, {{Automatic, Lighter@LightGray}}}, 

   Spacings -> {1, 2}, Dividers -> All]
Out[2]=