On Crofton-Glaisher type relations and derivation of generating functions for Hermite polynomials including the multi-index case

被引：18

作者：

Dattoli, G. ^{[1
]}

Khan, Subuhi ^{[2
]}

Ricci, P. E. ^{[3
]}

机构：

[1] ENEA, Ctr Ric Frascati, Unita Tecn Sci Tecnol Fis Avanzate, Grp Fis Teor & Matemat Applicata, I-00044 Frascati, Italy

[2] Aligarh Muslim Univ, Dept Math, Aligarh 202002, Uttar Pradesh, India

[3] Univ Roma La Sapienza, Dipartimento Matemat G Castelnuovo, I-00185 Rome, Italy

来源：

INTEGRAL TRANSFORMS AND SPECIAL FUNCTIONS | 2008年 / 19卷 / 01期

关键词：

exponential operator; Hermite polynomials; Glaisher and Crofton rules;

D O I：

10.1080/10652460701358984

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The Glaisher rule is an operational identity involving the action of an exponential operator containing the second-order derivatives acting on an exponential function. We use the Crofton and monomiality formalism to derive generalized forms to the multi-dimensional case and show its usefulness in the derivation of old and new forms of generating functions for a wealth of Hermite polynomials families.

引用

页码：1 / 9

页数：9

共 10 条

[1]

Andrews L. C., 1985, SPECIAL FUNCTIONS EN

[2]

[Anonymous], 1999, ADV SPECIAL FUNCTION

[3]

Appell P., 1926, Fonctions Hypergeometriques et Hyperspheriques: Polynomes d'Hermite

[4]

Crofton M.W., 1879, Q J MATH, V16, P323

[5] Operational methods, fractional operators and special polynomials [J].

Dattoli, G .

APPLIED MATHEMATICS AND COMPUTATION, 2003, 141 (01) :151-159

[6] Incomplete 2D Hermite polynomials: properties and applications [J].

Dattoli, G .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2003, 284 (02) :447-454

[7]

Dattoli G, 1997, RIV NUOVO CIMENTO, V20, P1

[8]

Roman S., 1984, Volume 111 of Pure and Applied Mathematics

[9]

Srivastava H.M., 1984, a Treatise on Generating Functions

[10] Hermite and Laguerre 2D polynomials [J].

Wünsche, A .

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2001, 133 (1-2) :665-678

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