《Polynomial Expansions of Analytic Functions》

Chapter Ⅰ．Introduction1

1．Generalities1

2．Representation formulas with a kernel4

3．The method of kernel expansion10

4．Lidstone series13

5．A set of Laguerre polynomials16

6．Generalized Appell polynomials17

Chapter Ⅱ．Representation of entire functions21

7．General theory21

8．Multiple expansions24

9．Appell polynomials28

（ⅰ）Bernoulli polynomials and generalizations29

（ⅱ）A set of Laguerre polynomials31

（ⅲ）Hermite polynomials31

（ⅳ）Reversed Laguerre polynomials32

（ⅴ）Reversed Rainville polynomials32

10．Sheffer polynomials33

（ⅵ）General difference polynomials34

（ⅶ）Poisson-Charlier,Narumi and Boole polynomials37

（ⅷ）Mittag-Leffler polynomials38

（ⅸ）Abel interpolation series38

（ⅹ）Laguerre polynomials40

（ⅹⅰ）Angelescu polynomials41

（ⅹⅱ）Denisyuk polynomials41

（ⅹⅲ）Squared Hermite polynomials41

（ⅹⅳ）Adhoc polynomials41

（ⅹⅴ）Actuarial polynomials42

11．More general polynomials42

（ⅹⅵ）Special hypergeometric polynomials43

（ⅹⅶ）Reversed Bessel polynomials43

（ⅹⅷ）q-difference polynomials44

（ⅹⅸ）Reversed Hermite polynomials45

（ⅹⅹ）Rain ville polynomials46

12．Polynomials not in generalized Appell form46

Chapter Ⅲ．Representation of functions that are regular at the origin47

13．Integral representations47

14．Brenke polynomials51

（ⅰ）Polynomials generated by A(w)(1-zw)-λ52

（ⅱ）q-difference polynomials54

15．More general polynomials55

16．Polynomials generated by A(w)(1-zg(w))-λ57

（ⅲ）Taylor series57

（ⅳ）Lerch polynomials57

（ⅴ）Gegenbauer polynomials58

（ⅵ）Chebyshev polynomials58

（ⅶ）Humbert polymomials58

（ⅷ）Faber polynomials59

17．Special hypergeometric polynomials60

（ⅸ） Jacobi polynomials60

18．Polynomials not in generalized Appell form61

Chapter Ⅳ．Applications66

19．Uniqueness theorems66

20．Functional equations67

Bibliography71

Index75