González, Beatriz; Kalla, Shyam L. A generalization of the Hermite polynomials. (Spanish. English summary) Zbl 0770.33006 Rev. Téc. Fac. Ing., Univ. Zulia 15, No. 2, 143-145 (1992). The authors define the polynomials \(H_{2n+r,\alpha}(x)\), \(n=0,1,\dots,\alpha>-1\) and \(r\) a fixed non-negative integer, by the relation \[ H_{2n+r,\alpha}(x)={(-1)^ n(2n+r)!\over n!} (2x)^ r\Phi(-n,\alpha+1;x^ 2), \] where \(\Phi\) is the confluent hypergeometric function. If \(r=0\) and \(\alpha=-1/2\) and \(\alpha=1/2\) these polynomials reduce to the classical Hermite polynomials \(H_{2n}(x)\) or \(H_{2n+1}(x)\) respectively. Series expansion, generating function, recurrence relation, orthogonality property and other properties of the polynomials \(H_{2n+r,\alpha}(x)\) are obtained. Reviewer: L.Gatteschi (Torino) Cited in 1 Review MSC: 33C45 Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) Keywords:Hermite polynomials PDFBibTeX XMLCite \textit{B. González} and \textit{S. L. Kalla}, Rev. Téc. Fac. Ing., Univ. Zulia 15, No. 2, 143--145 (1992; Zbl 0770.33006) Digital Library of Mathematical Functions: §15.15 Sums ‣ Properties ‣ Chapter 15 Hypergeometric Function §15.19(i) Maclaurin Expansions ‣ §15.19 Methods of Computation ‣ Computation ‣ Chapter 15 Hypergeometric Function