Contributions to the Problem of Approximation of Equidistant Data by Analytic Functions

Part B—On the Problem of Osculatory Interpolation. A Second Class of Analytic Approximation Formulae
  • I. J. Schoenberg
Part of the Contemporary Mathematicians book series (CM)


The present second part of the paper has two objectives. Firstly, we wish to carry further the important actuarial work on the subject of osculatory interpolation (Chapters I and II). Secondly, we construct even analytic functions L(x), of extremely fast damping rate, such that the interpolation formula of cardinal type
$$F\left( x \right)\, = \,\sum\limits_{v = - \infty }^\infty {y_v L\left( {x - v} \right)}$$
reproduces polynomials of a certain degree and reduces to a smoothing formula for integral values of the variable x (Chapter III). This second problem is found to be intimately connected with the subject of osculatory interpolation.


Basic Function Characteristic Function Regular Function Interpolation Formula Polation Formula 
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Copyright information

© Springer Science+Business Media New York 1988

Authors and Affiliations

  • I. J. Schoenberg
    • 1
  1. 1.Ballistic Research LaboratoriesUniversity of Pennsylvania, Aberdeen Proving GroundUSA

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