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On Properties of Hermite And Q-hermıte I Polynomials and Theır Limit Relations

BROWSE_DETAIL_CREATION_DATE: 08-06-2017

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BROWSE_DETAIL_TYPE: Thesis

BROWSE_DETAIL_SUB_TYPE: Masters

BROWSE_DETAIL_PUBLISH_STATE: Unpublished

BROWSE_DETAIL_FORMAT: PDF Document

BROWSE_DETAIL_LANG: English

BROWSE_DETAIL_SUBJECTS: Mathematics,

BROWSE_DETAIL_CREATORS: Alwashi, Sakina Abdusalam Ahmed (Author),

BROWSE_DETAIL_CONTRIBUTERS: Turan, Mehmet (Advisor),

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Classical ortohogonal polynomials, Hermite polynomials, q-classical orthogonalpolynomials, discrete q-Hermite I polynomials, dierential equation of hypergeometrictype, q-dierence equation of hypergeometric type, Rodrigues formula,three terms recurrence relation, generating function


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In this thesis, some important properties of the Hermite polynomials and discrete q-Hermite I polynomials are presented. Their properties will be considered in the samemanner. The discrete q-Hermite I polynomials are the q-analogues of the Hermitepolynomials. Such polynomials are an important class of the classical orthogonalpolynomials and their q-analogues. The central idea in this thesis is to study the differentialand q-dierence equation of hypergeometric type, three terms recurrencerelations, Rodrigues formulas, orthogonalities and generating functions that the Hermitepolynomials and its discrete version have. Hermite polynomials are obtainedfrom the discrete q-Hermite I polynomials in the limiting case as q ! 1: Such limitrelation between the Hermite polynomials and the discrete q-Hermite I polynomialson each properties that is introduced in the thesis are considered in detailed.


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