盖根鲍尔多项式 Gegenbauer polynomials

（重定向自Ultraspherical polynomial）

盖根鲍尔多项式 $C_n^{(\alpha)}$ 又称超球多项式，是定义在区间 $[-1,1]$ 上、权函数为 $(1-x^2)^{\alpha-1/2}$ 的正交多项式。它是勒让德多项式和切比雪夫多项式的推广，又是雅可比多项式的特殊情况。它以奥地利数学家Leopold Gegenbauer命名。

单词	Ultraspherical polynomial
释义	Ultraspherical polynomial 中文百科盖根鲍尔多项式 Gegenbauer polynomials （重定向自Ultraspherical polynomial）盖根鲍尔多项式 $C_n^{(\alpha)}$ 又称超球多项式，是定义在区间 $[-1,1]$ 上、权函数为 $(1-x^2)^{\alpha-1/2}$ 的正交多项式。它是勒让德多项式和切比雪夫多项式的推广，又是雅可比多项式的特殊情况。它以奥地利数学家Leopold Gegenbauer命名。英语百科 Gegenbauer polynomials 盖根鲍尔多项式（重定向自Ultraspherical polynomial） In mathematics, Gegenbauer polynomials or ultraspherical polynomials C(α) n(x) are orthogonal polynomials on the interval [−1,1] with respect to the weight function (1 − x). They generalize Legendre polynomials and Chebyshev polynomials, and are special cases of Jacobi polynomials. They are named after Leopold Gegenbauer.
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Ultraspherical polynomial