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In this paper, for the proposed extended Laguerre polynomials  A α q , n x , the generalized hypergeometric function of the type  F q q , q &gt; 2 and extension of the Laguerre polynomial are introduced. Similar to those related to the Laguerre polynomials, the generating function, recurrence relations, and Rodrigue’s formula are determined. Some corollaries are also discussed at the end.

journal of function spaces

The Extended Laguerre Polynomials <math xmlns="http://www.w3.org/1998/Math/MathML" id="M1"> <mfenced open="{" close="}"> <mrow> <msubsup> <mrow> <mi>A</mi> </mrow> <mrow> <mi>q</mi> <mo>,</mo> <mi>n</mi> </mrow> <mrow> <mfenced open="(" close=")"> <mrow> <mi>α</mi> </mrow> </mfenced> </mrow> </msubsup> <mfenced open="(" close=")"> <mrow> <mi>x</mi> </mrow> </mfenced> </mrow> </mfenced> </math> Involving <math xmlns="http://www.w3.org/1998/Math/MathML" id="M2"> <msub> <mrow> <mmultiscripts> <…

The Extended Laguerre Polynomials A q , n α x Involving <…

The Extended Laguerre Polynomials $\{A_{q, n}^{(α)} (x)\}$ Involving ${<…}$