Synopsis
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.- 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-Leffier 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) Rainville polynomials.- § 12. Polynomials not in generalized Appell form.- III. Representation of functions that are regular at the origin.- § 13. Integral representations.- § 14. Brenke polynomials.- (i) Polynomials generated by A(?) (1 - z?)-?.- (ii) q-difference polynomials.- § 15. More general polynomials.- § 16. Polynomials generated by A(?) (1 - zg(?))-?.- (iii) Taylor series.- (iv) Lerch polynomials.- (v) Gegenbauer polynomials.- (vi) Chebyshev polynomials.- (vii) Humbert polynomials.- (viii) Faber polynomials.- § 17. Special hypergeometric polynomials.- (ix) Jacobi polynomials.- § 18. Polynomials not in generalized Appell form.- IV. Applications.- § 19. Uniqueness theorems.- § 20. Functional equations.
Les informations fournies dans la section « Synopsis » peuvent faire référence à une autre édition de ce titre.
