连续勒让德多项式是一个以基本超几何函数定义的正交多项式[1]
极限关系[编辑]
令连续q勒让德多项式 q->1 得勒让德多项式
- 验证5阶连续q勒让德多项式→勒让德多项式
由定义,
求 q→1 的极限值:
而5阶勒让德多项式为:
两者显然相等,所以
验证毕
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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参考文献[编辑]
- ^ Roelof Koekoek, Hypergeometric Orthogonal Polynomials and its q-Analogues, p475,Springer,2010