Chapter Ⅰ．Introduction

1．Generalities

2．Representation formulas with a kernel

3．The method of kernel expansion

4．Lidstone series

5．A set of Laguerre polynomials

6．Generalized Appell polynomials

Chapter Ⅱ．Representation of entire functions

7．General theory

8．Multiple expansions

9．Appell polynomials

（ⅰ）Bernoulli polynomials and generalizations

（ⅱ）A set of Laguerre polynomials

（ⅲ）Hermite polynomials

（ⅳ）Reversed Laguerre polynomials

（ⅴ）Reversed Rainville polynomials

10．Sheffer polynomials

（ⅵ）General difference polynomials

（ⅶ）Poisson-Charlier,Narumi and Boole polynomials

（ⅷ）Mittag-Leffler polynomials

（ⅸ）Abel interpolation series

（ⅹ）Laguerre polynomials

（ⅹⅰ）Angelescu polynomials

（ⅹⅱ）Denisyuk polynomials

（ⅹⅲ）Squared Hermite polynomials

（ⅹⅳ）Adhoc polynomials

（ⅹⅴ）Actuarial polynomials

11．More general polynomials

（ⅹⅵ）Special hypergeometric polynomials

（ⅹⅶ）Reversed Bessel polynomials

（ⅹⅷ）q-difference polynomials

（ⅹⅸ）Reversed Hermite polynomials

（ⅹⅹ）Rain ville polynomials

12．Polynomials not in generalized Appell form

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

13．Integral representations

14．Brenke polynomials

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

（ⅱ）q-difference polynomials

15．More general polynomials

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

（ⅲ）Taylor series

（ⅳ）Lerch polynomials

（ⅴ）Gegenbauer polynomials

（ⅵ）Chebyshev polynomials

（ⅶ）Humbert polymomials

（ⅷ）Faber polynomials

17．Special hypergeometric polynomials

（ⅸ） Jacobi polynomials

18．Polynomials not in generalized Appell form

Chapter Ⅳ．Applications

19．Uniqueness theorems

20．Functional equations

Bibliography

Index