q拉蓋爾多項式是一個以基本超幾何函數和Q階乘冪定義的正交多項式
q-Laguerre Polynomials
![{\displaystyle \displaystyle L_{n}^{(\alpha )}(x;q)={\frac {(q^{\alpha +1};q)_{n}}{(q;q)_{n}}}{}_{1}\phi _{1}(q^{-n};q^{\alpha +1};q,-q^{n+\alpha +1}x)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/9c5f570c260493ffa4a54976b33fc686a51ffc1e)
Q-拉蓋爾多項式滿足下列正交關係
![{\displaystyle \int _{a}^{b}\!L_{n}^{(\alpha )}(x;q)*L_{m}^{(\alpha )}(x;q)*(x^{\alpha })/(-x;q)_{\infty }\,dx={\frac {(q^{\alpha }+1;q)_{n}}{(q;q)_{n}*q^{n}}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/7e6a7d95e28dfe27569e0877c8241649ad25322d)
- 小q雅可比多項式→Q拉蓋爾多項式.
在校q雅可比多項式的定義中,令
以及
,並令
,即得q拉蓋爾多項式。
- Q梅西納多項式→Q拉蓋爾多項式;
令Q梅西納多項式中
,以及
,然後取
即得Q拉蓋爾多項式。
下列 :
圖,以q 為可變參數。
Q-LAGUERRE POLYNOMIALS ABS COMPLEX 3D MAPLE PLOT
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Q-LAGUERRE POLYNOMIALS IM COMPLEX 3D MAPLE PLOT
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Q-LAGUERRE POLYNOMIALS RE COMPLEX 3D MAPLE PLOT
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Q-LAGUERRE POLYNOMIALS ABS DENSITY MAPLE PLOT
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Q-LAGUERRE POLYNOMIALS RE DENSITY MAPLE PLOT
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Q-LAGUERRE POLYNOMIALS IM DENSITY MAPLE PLOT
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