C2的四类正交多项式及正弦和余弦函数的对称和反对称推广
Four families of orthogonal polynomials of C2 and symmetric and antisymmetric generalizations of sine and cosine functions
摘要：
最近引入了三角函数的四个推广族。本文将这类函数转化为四类二元正交多项式。给出了多项式构造的递推关系。找到了这四类多项式的渐近关系以及相应的权函数。最低阶多项式的表被示出。发现了许多类三角恒等式，其中两个函数族被证明是紧李群Sp（4）的有限维不可约表示的Weyl特征标公式中遇到的函数。其他两个家庭的职能似乎没有发挥任何作用，李理论迄今为止，尽管他们类似的“好”的性质。
英文摘要：
Four families of generalizations of trigonometric functions were recently introduced. In the paper the functions are transformed into four families of orthogonal polynomials depending on two variables. Recurrence relations for construction of the polynomials are presented. Orthogonality relations of the four families of polynomials are found together with the appropriate weight fuctions. Tables of the lowest degree polynomials are shown. Numerous trigonometric-like identities are found. Two of the four families of functions are identified as the functions encountered in the Weyl character formula for the finite dimensional irreducible representations of the compact Lie group Sp(4). The other two families of functions seem to play no role in Lie theory so far in spite of their analogous `good' properties.
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