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Certain generating funtion of generalized Apostol type Legendre-based polynomials


Abstract


In this paper, we aim to introduce a generating function for generalized Apostol type Legendre-Based polynomials which extends some known results. We also deduce some properties of the generalized Apostol-Bernoulli polynomials, the generalized Apostol-Euler polynomials and the generalized Apostol-Genocchi polynomials of higher order. By making use of the generating function method and some functional equations mentioned in the paper, we conduct a further investigation in order to obtain some implicit summation formulae and general symmetry identities for the generalized Apostol type Legendre-Based polynomials.

DOI Code: 10.1285/i15900932v37n2p21

Keywords: Hermite polynomials and their two variable extensions; generalized Apostol Bernoulli numbers and polynomials; generalized Apostol Euler numbers and polynomials; generalized Apostol Genocchi numbers and polynomials; Legendre polynomials and their two variable extensions; 0th order Tricomi function; generalized Apostol type Legendre-Based polynomials; summation formulae; symmetric identities

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