# zbMATH — the first resource for mathematics

##### Examples
 Geometry Search for the term Geometry in any field. Queries are case-independent. Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact. "Topological group" Phrases (multi-words) should be set in "straight quotation marks". au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted. Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff. "Quasi* map*" py: 1989 The resulting documents have publication year 1989. so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14. "Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic. dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles. py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses). la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

##### Operators
 a & b logic and a | b logic or !ab logic not abc* right wildcard "ab c" phrase (ab c) parentheses
##### Fields
 any anywhere an internal document identifier au author, editor ai internal author identifier ti title la language so source ab review, abstract py publication year rv reviewer cc MSC code ut uncontrolled term dt document type (j: journal article; b: book; a: book article)
Operational identities and properties of ordinary and generalized special functions. (English) Zbl 0943.33005
Here the theory of Hermite, Laguerre, and of the associated generating functions is reformulated within the framework of an operational formalism. This point of view provides more efficient tools which allow the straightforward derivation of a number of new and old identities. In this paper a central role is played by negative derivative operators and by their link with the Tricomi functions and the generalized Laguerre polynomials.

##### MSC:
 33C45 Orthogonal polynomials and functions of hypergeometric type
Full Text:
##### References:
 [1] Dattoli, G.; Ottaviani, P. L.; Torre, A.; Vazquez, L.: Evolution operator equations: integration with algebraic and finite difference methods. Applications to physical problems in classical and quantum mechanics and quantum field theory. Rivista nuovo cimento 20, 1-133 (1997) [2] Dattoli, G.; Lorenzutta, S.; Torre, A.: Miscellaneous identities of generalized Hermite polynomials. Matematiche 52, 337-343 (1997) · Zbl 0934.33009 [3] Dattoli, G.; Torre, A.; Carpanese, M.: Operational rules and arbitrary order Hermite generating functions. J. math. Anal. appl. (1998) · Zbl 0918.33012 [4] Burchnall, J. L.: Quart. J. Math. Oxford series (2). 12, 9-11 (1941) [5] Appell, P.; Fériet, J. Kampé-De: Fonctions hypergéométriques et hypersphériques, polynomes d’hermite. (1926) [6] Bell, E. T.: Ann. of math.. 35, 258-277 (1934) [7] Dattoli, G.; Torre, A.: Theory and applications of generalized Bessel functions. (1996) [8] Srivastava, H.; Manocha, M.: A treatise on generating functions. (1984) · Zbl 0535.33001