Turkish Journal of Mathematics




Motivated by their importance and potential for applications in a variety of research fields, recently, various polynomials and their extensions have been introduced and investigated. In this sequel, we modify the known generating functions of polynomials, due to both Milne-Thomson and Dere and Simsek, to introduce a new class of generalized polynomials and present some of their involved properties. As obvious special cases of the newly introduced polynomials, we also introduce so-called power sum-Laguerre--Hermite polynomials and generalized Laguerre and Euler polynomials and we present some of their involved identities and formulas. The results presented here, being very general, are pointed out to be specialized to yield a number of known and new identities involving relatively simple and familiar polynomials.


Milne-Thomson polynomials, Dere-Simsek polynomials, Laguerre polynomials, Hermite polynomials, Euler polynomials, generalized Laguerre-Euler polynomials, sum of integer powers, summation formulae, symmetric identities

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