摘要：In this paper, we investigate some interesting identities on the Bernoulli, Euler, Hermite and generalized Gegenbauer polynomials arising from the orthogonality of generalized Gegenbauer polynomials in the generalized inner product 〈 p 1 ( x ) , p 2 ( x ) 〉 = ∫ − α q p α q p ( α q − p 2 x 2 ) λ − 1 2 p 1 ( x ) p 2 ( x ) d x . $$\bigl\langle {{p_)}(x),{p_,}(x)} \bigr\rangle = \int_{ - \frac{{\sqrt{\alpha q}}}{p}}^{\frac{{\sqrt{ \alpha q} }}{p}} {{\bigl(\alpha q - p^,{x^,}\bigr)}^{\lambda - \frac),}} {p_)}(x){p_,}(x)\,dx. $$
关键词：generalized Gegenbauer polynomials ; orthogonality ; generalized inner product space
