Generalized Taylor expansions Euler-Maclaurin summation formula

Elementary Theory and Philip Spain ()
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Philip Spain: University of Glasgow, Department of Mathematics

Chapter Chapter VI in Elements of Mathematics Functions of a Real Variable, 2004, pp 269-303 from Springer

Abstract: Abstract Let K be a commutative field of characteristic 0, and K[X] the algebra of polynomials in one indeterminate over K (Alg., IV. 1); throughout this section by anoperator on K[X] we shall mean a linear map U of the vector space K[X] (over K) into itself; since the monomials X n (n≥0) form a basis for this space, U is determined by the polynomials U(X n ); specifically, if $$f({\text{X}}) = \sum\limits_{k = 0}^\infty {{\lambda _k}} {{\text{X}}^k}$$ with λ k ∈K, then $$U(f) = \sum\limits_{k = 0}^\infty {{\lambda _k}U} {\text{(}}{{\text{X}}^k})$$

Keywords: Asymptotic Expansion; Prime Number; Composition Operator; Formal Series; Entire Series (search for similar items in EconPapers)
Date: 2004
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DOI: 10.1007/978-3-642-59315-4_7

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