連續勒讓德多項式是一個以基本超幾何函數定義的正交多項式[1]
極限關係
令連續q勒讓德多項式 q->1 得勒讓德多項式
- 驗證5階連續q勒讓德多項式→勒讓德多項式
由定義,
求 q→1 的極限值:
而5階勒讓德多項式為:
兩者顯然相等,所以
驗證畢
圖集
CONTINUOUS Q-LEGENDER POLYNOMIALS ABS COMPLEX 3D MAPLE PLOT
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CONTINUOUS Q-LEGENDER POLYNOMIALS IM COMPLEX 3D MAPLE PLOT
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CONTINUOUS Q-LEGENDER POLYNOMIALS RE COMPLEX 3D MAPLE PLOT
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CONTINUOUS Q-LEGENDER POLYNOMIALS ABS DENSITY MAPLE PLOT
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CONTINUOUS Q-LEGENDER POLYNOMIALS IM DENSITY MAPLE PLOT
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CONTINUOUS Q-LEGENDER POLYNOMIALS RE DENSITY MAPLE PLOT
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參考文獻
- ^ Roelof Koekoek, Hypergeometric Orthogonal Polynomials and its q-Analogues, p475,Springer,2010