大q-勒让德多项式的加法公式
Addition formula for big q-Legendre polynomials
摘要：
从Koornwinder关于大$q$ -勒让德多项式为量子$SU(2)$群上的球元的解释出发，导出了大$q$ -勒让德多项式的加法公式.该公式涉及Al-Salam-Carlitz多项式、小$q$ -雅可比多项式和对偶$q$ -Krawtchouk多项式。对于小的$q$ -超球多项式，一个关于大的$q$ -勒让德多项式的乘积公式后面是$q$ -积分.当$q$趋于1时，得到了勒让德多项式的加法和乘积公式。
英文摘要：
From Koornwinder's interpretation of big $q$-Legendre polynomials as spherical elements on the quantum $SU(2)$ group an addition formula is derived for the big $q$-Legendre polynomial. The formula involves Al-Salam--Carlitz polynomials, little $q$-Jacobi polynomials and dual $q$-Krawtchouk polynomials. For the little $q$-ultraspherical polynomials a product formula in terms of a big $q$-Legendre polynomial follows by $q$-integration. The addition and product formula for the Legendre polynomials are obtained when $q$ tends to 1.
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