Hypergeometric term

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Efficient algorithms for construction of recurrence relations for the expansion and connection coefficients in series of quantum classical orthogonal polynomials

Formulae expressing explicitly the q-difference derivatives and the moments of the polynomials Pn(x ; q) ∈ T (T ={Pn(x ; q) ∈ Askey–Wilson polynomials: Al-Salam-Carlitz I, Discrete q-Hermite I, Little (Big) q-Laguerre, Little (Big) q-Jacobi, q-Hahn, Alternative q-Charlier) of any degree and for any order in terms of Pi(x ; q) themselves are proved. We will also provide two other interesting formulae to expand the coefficients of general-order q-difference derivatives Dp q f (x), and for the moments xDp q f (x), of an arbitrary function f(x) in terms of its original expansion coefficients.

15p kethamoi1 20-11-2019 14 0 Download

Formal residue and computer-assisted proofs of combinatorial identities

Many combinatorial numbers can be represented by the formal residues of hypergeometric terms. With these representations and the extended Zeilberger algorithm, we generate recurrence relations for summations involving combinatorial sequences such as Stirling numbers and their q -analog. As examples, we give computer proofs of several known identities and derive some new identities. The applicability of this method is also studied.

15p nutifooddau 21-01-2019 13 1 Download