Study On Combinatorial Identities Of Some Sequences Of Numbers And Polynomials

In this thesis,by applying the generating function methods,Pade approximation techniques and summation transform techniques,we perform a further investigation for the Frobenius-Euler polynomials,Derangements numbers,Bell numbers and the generalized Laguerre polynomials,and establish some combinatorial identities for the polynomials and numbers.These results presented here improve and generalize the corresponding methods and results showed in the reference.This thesis is organized as follows.1.By making use of the generating function methods and summation transform techniques,we drive a study for the Frobenius-Euler and establish some convolutions for them.It turns out that some well-known results from Carlitz can be obtained as special cases,and some Kim's results for the Bernoulli polynomials can be generalized to the case of the Frobenius-Euler polynomials.2.By using the generating function methods and Pade approximation techniques,a further investigation for the number of Derangements and Bell numbers is performed,some new recurrence formulae for them are established,by virtue of which,a closed formula for the number of Derangements is deduced,and Clarke and Sved's identities on the number of Derangements and Bell numbers are implied.3.By applying the generating function methods and Pad6 approximation tech-niques,we perform a further investigation for the generalized Laguerre polynomials and establish some new combinatorial identities for them.It turns out that some known closed formulae due to Dattoli and Moya are obtained as special cases.