The \(K\) extended Laguerre polynomials involving \(\left\{A^{(\alpha)}_{r, n, k}(x)\right\}{}_rf_r\), \(r > 2\). (English) Zbl 1528.33007
Summary: In this manuscript, we present the generalized hypergeometric function of the type \({}_rF_r,r>2\) and extension of the \(K\) Laguerre polynomial for the \(K\) extended Laguerre polynomials \(\left\{ A_{r , n , k}^{\left( \alpha\right)} \left( x\right)\right\}\). Additionally, we describe the \(K\) generating function, \(K\) recurrence relations, and \(KS\) Rodrigues formula.
MSC:
| 33C20 | Generalized hypergeometric series, \({}_pF_q\) |
| 33C45 | Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) |
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