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Generalized Taylor expansions Euler-Maclaurin summation formula

  • Elementary Theory
  • Philip Spain

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 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Elementary Theory
  • Philip Spain
    • 1
  1. 1.Department of MathematicsUniversity of GlasgowGlasgowScotland

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