Error Inequalities in Polynomial Interpolation and Their Applications

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See our disclaimer. Customer Reviews. Costabile [15] , [16] also gave a new form of Bernoulli polynomials, called determinantal form, and later these ideas have been extended to Appell polynomial sequences. In fact, in , Costabile and Longo [17] proposed an algebraic and elementary approach to Appell polynomial sequences. At the same time, Yang and Youn [18] also gave an algebraic approach, but with different methods.

The approach to Appell polynomial sequences via linear algebra is an easily comprehensible mathematical tool, specially for non-specialists; that is very good because many polynomials arise in physics, chemistry and engineering. Then we have. The function a h is said, by Appell, 'generating function' of the sequence A n x n. He also considered [1] an application of these polynomial sequences to linear differential equations, which is out of this context.

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Bernoulli polynomials [23] , [17] :. Euler polynomials [23] , [17] :. Normalized Hermite polynomials [24] , [17] :. Laguerre polynomials [24] , [17] :. Generalized Hermite polynomials [17] :. Generalized Laguerre polynomials [17] :. Expanding the determinant A B n x with respect to the first row we obtain. Then the following are inverse relations:. Thus we finally obtain. Then the following relations holds:.

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In fact we get. The polynomial sequence.

In virtue of this it is possible to obtain a dual theory of Appell polynomials of first kind, in the sense that similar properties can be proven [20]. Bernoulli polynomials of second kind [23] , [20] :. Boole polynomials [23] , [20] :. Let X be the linear space of real functions defined in the interval [ 0 , 1 ] continuous and with continuous derivatives of all necessary orders. Remark 8 The generating function of the sequence A L , n x is. Then, we have. Volume 33 Issue 4 Oct , pp.

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