ABSTRACT

By using the three-term recurrence relation for orthogonal polynomials, we produce a collection of two-dimensional contiguous relations for certain generalized hypergeometric functions. These generalized hypergeometric functions arise through linearization coefficients for some classical orthogonal polynomials in the Askey-scheme, namely Gegenbauer (ultraspherical), Hermite, Jacobi and Laguerre polynomials.

中文翻译：

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经典正交多项式线性化系数的二维连续关系

摘要

通过使用正交多项式的三项递推关系，我们为某些广义超几何函数生成二维连续关系的集合。这些广义超几何函数是通过 Askey 方案中一些经典正交多项式的线性化系数产生的，即 Gegenbauer（超球面）、Hermite、Jacobi 和 Laguerre 多项式。