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For polynomial sequence of binomial type we propose a new recurrence formula equivalent to a determinantal form of the sequence, from which known and unknown properties are deducted. Relationships whit $${\delta}$$ δ –functionals, $${\delta}$$ δ –operators and generating function are pointed out. Finally, some classical examples are studied, highlighting interesting determinantal...
A Birkhoff interpolation problem is studied. The explicit solution and estimation of remainder is given. The cases of equidistant and Chebyshev nodes are considered. This problem is of interest in collocation methods of boundary value problem (Costabile and Napoli in Far East J. Appl. Math. 25(3):289–305, 2006; Costabile and Longo in Applied and Industrial Mathematics in Italy III, 2009, in press)...
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