《INTERPOLATORY FUNCTION THEORY》求取 ⇩

INTRODUCTION1

1.Preliminary results1

CHAPTER I.SERIES OF POLYNOMIALS4

2.Basic sets of polynomials4

3.The convergence of basic series10

CHAPTER Ⅱ.THE SUM OF A FUNCTION17

4.Bernoulli polynomials17

5.The sum of a function21

6.Linear difference equations30

CHAPTER Ⅲ. PROPERTIES OF SUCCESSIVE DERIVATIVES32

7.A theorem of Polya32

8.Theorems of Gontcharoff, Takenaka and Kakeya38

9.The two-point boundary problem45

CHAPTER Ⅳ. INTERPOLATION AT THE INTEGERS52

10.The Gregory-Newton series52

11.The Newton-Gauss series and the cardinal series62

CHAPTER V.INTERPOLATION AT THE LATTICE POINTS72

12.The two-dimensional cardinal series72

13.The “flat”regions of integral and meromorphic functions73

CHAPTER VI. ASYMPTOTIC PERIODS84

14.Integral functions84

15.Meromorphic functions95

Bibliography102

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