# Sinc-Related Methods

Chapter

## Abstract

The formulas of the previous chapter are all related to the Cardinal function representation ; with \({z_k}\, = \,{\phi ^{ - 1}}(kh)\). We recall here, that\(C(F,h)\, \circ \,\phi \) both interpolates

$$C(f,\,h)\, \circ \,\phi (x)\, = \,\mathop \sum \limits_{k = - \infty }^\infty \,F({z_k})\,S(k,h)\, \circ \,\phi (x),$$

(5.1.1)

*F*on Г = φ^{−1}(R) , and it also accurately approximates it in a suitable space of functions. In the present chapter we examine some related methods of approximation. This chapter may be termed*the unfinished chapter*, in the sense that many other formulas are possible by each approach presented here, although we do not present or study the majority of these as we have done in the case of the Cardinal expansion; indeed, a thorough study, as done in the case of Sinc methods in this text would require the writing of at least an additional text. We have merely chosen to point out some connections of Sinc formulas with other formulas, thus opening doors to new avenues of research, and to present some esthetically pleasing formulas which may have practical value as well.## Keywords

Rational Function Elliptic Function Continue Fraction Pade Approximant Pade Approximation
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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## Copyright information

© Springer-Verlag New York, Inc. 1993