Polynomial Expansions of Analytic FunctionsPDF电子书下载

Chapter Ⅰ．Introduction 1

1．Generalities 1

2．Representation formulas with a kernel 4

3．The method of kernel expansion 10

4．Lidstone series 13

5．A set of Laguerre polynomials 16

6．Generalized Appell polynomials 17

Chapter Ⅱ．Representation of entire functions 21

7．General theory 21

8．Multiple expansions 24

9．Appell polynomials 28

（ⅰ）Bernoulli polynomials and generalizations 29

（ⅱ）A set of Laguerre polynomials 31

（ⅲ）Hermite polynomials 31

（ⅳ）Reversed Laguerre polynomials 32

（ⅴ）Reversed Rainville polynomials 32

10．Sheffer polynomials 33

（ⅵ）General difference polynomials 34

（ⅶ）Poisson-Charlier,Narumi and Boole polynomials 37

（ⅷ）Mittag-Leffler polynomials 38

（ⅸ）Abel interpolation series 38

（ⅹ）Laguerre polynomials 40

（ⅹⅰ）Angelescu polynomials 41

（ⅹⅱ）Denisyuk polynomials 41

（ⅹⅲ）Squared Hermite polynomials 41

（ⅹⅳ）Adhoc polynomials 41

（ⅹⅴ）Actuarial polynomials 42

11．More general polynomials 42

（ⅹⅵ）Special hypergeometric polynomials 43

（ⅹⅶ）Reversed Bessel polynomials 43

（ⅹⅷ）q-difference polynomials 44

（ⅹⅸ）Reversed Hermite polynomials 45

（ⅹⅹ）Rain ville polynomials 46

12．Polynomials not in generalized Appell form 46

Chapter Ⅲ．Representation of functions that are regular at the origin 47

13．Integral representations 47

14．Brenke polynomials 51

（ⅰ）Polynomials generated by A(w)(1-zw)-λ 52

（ⅱ）q-difference polynomials 54

15．More general polynomials 55

16．Polynomials generated by A(w)(1-zg(w))-λ 57

（ⅲ）Taylor series 57

（ⅳ）Lerch polynomials 57

（ⅴ）Gegenbauer polynomials 58

（ⅵ）Chebyshev polynomials 58

（ⅶ）Humbert polymomials 58

（ⅷ）Faber polynomials 59

17．Special hypergeometric polynomials 60

（ⅸ） Jacobi polynomials 60

18．Polynomials not in generalized Appell form 61

Chapter Ⅳ．Applications 66

19．Uniqueness theorems 66

20．Functional equations 67

Bibliography 71

Index 75