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- W2962998156 abstract "In this paper we introduce the polynomials { d n ( r ) ( x ) } and { D n ( r ) ( x ) } given by d n ( r ) ( x ) = ∑ k = 0 n ( x + r + k k ) ( x − r n − k ) ( n ≥ 0 ) , D 0 ( r ) ( x ) = 1 , D 1 ( r ) ( x ) = x and D n + 1 ( r ) ( x ) = x D n ( r ) ( x ) − n ( n + 2 r ) D n − 1 ( r ) ( x ) ( n ≥ 1 ) . We show that { D n ( r ) ( x ) } are orthogonal polynomials for r > − 1 2 , and establish many identities for { d n ( r ) ( x ) } and { D n ( r ) ( x ) } , especially obtain a formula for d n ( r ) ( x ) 2 and the linearization formulas for d m ( r ) ( x ) d n ( r ) ( x ) and D m ( r ) ( x ) D n ( r ) ( x ) . As an application we extend recent work of Sun and Guo." @default.
- W2962998156 created "2019-07-30" @default.
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- W2962998156 date "2017-12-01" @default.
- W2962998156 modified "2023-10-11" @default.
- W2962998156 title "A kind of orthogonal polynomials and related identities" @default.
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- W2962998156 doi "https://doi.org/10.1016/j.jmaa.2017.07.049" @default.
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