Derivation of the Hille-Hardy type formulae and operational methods
- Volume: 14, Issue: 2, page 85-90
- ISSN: 1120-6330
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topDattoli, Giuseppe. "Derivation of the Hille-Hardy type formulae and operational methods." Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni 14.2 (2003): 85-90. <http://eudml.org/doc/252289>.
@article{Dattoli2003,
abstract = {The Hille-Hardy formula is a bilinear generating function, involving products of Laguerre polynomials. We use the point of view, developed in previous publications, to propose an operational method which allows a fairly direct derivation of this kind of formulae.},
author = {Dattoli, Giuseppe},
journal = {Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni},
keywords = {Operational methods; Hermite polynomials; Laguerre polynomials; Bilinear generating functions},
language = {eng},
month = {6},
number = {2},
pages = {85-90},
publisher = {Accademia Nazionale dei Lincei},
title = {Derivation of the Hille-Hardy type formulae and operational methods},
url = {http://eudml.org/doc/252289},
volume = {14},
year = {2003},
}
TY - JOUR
AU - Dattoli, Giuseppe
TI - Derivation of the Hille-Hardy type formulae and operational methods
JO - Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
DA - 2003/6//
PB - Accademia Nazionale dei Lincei
VL - 14
IS - 2
SP - 85
EP - 90
AB - The Hille-Hardy formula is a bilinear generating function, involving products of Laguerre polynomials. We use the point of view, developed in previous publications, to propose an operational method which allows a fairly direct derivation of this kind of formulae.
LA - eng
KW - Operational methods; Hermite polynomials; Laguerre polynomials; Bilinear generating functions
UR - http://eudml.org/doc/252289
ER -
References
top- DATTOLI, G., Hermite-Bessel and Laguerre Bessel Functions, a by-product of the monomiality principle. In: D. COCOLICCHIO - G. DATTOLI - H.M. SRIVASTAVA (eds.), Proceedings of the Workshop on Special Functions and Applications in Mathematics and Physics (Melfi, 9-12 May 1999). Aracne Editrice, Roma2000. Zbl1022.33006MR1857483
- ANDREWS, L.C., Special Functions for Applied Mathematicians and Engineers. Mac Millan, New York1985. Zbl0920.33001MR779819
- DATTOLI, G., Generalized Polynomials, Operational Identities and their Applications. J. Comput. Appl. Math., 118, 2000, 111-123. Zbl1016.33012MR1765943DOI10.1016/S0377-0427(00)00283-1
- SRIVASTAVA, H.M. - MANOCHA, H.L., A Treatise on Generating Functions. J. Wiley, New York1984. For earlier derivations by Miller and Lebedeff, see e.g. ERDÉLYI, A. et al., Bateman Manuscript project, Vol. 2. Zbl0535.33001MR750112
- DATTOLI, G., Bilateral Generating Functions and Operational Methods. J. Math. Anal. and Appl., to appear. Zbl1073.33008MR1907139DOI10.1016/S0022-247X(02)00047-1
- KRINSKY, S. - GLUCKSTERN, R.L., Analysis of statistical correlations and intensity spiking in the self-amplified spontaneous-emission free-electron laser. Phys. Rev. ST Accel. Beams, 6(5), 2003, 050701-050710.
- DATTOLI, G. - RICCI, P.E., Multi-index Polynomials and Applications to Statistical Problems. To appear.
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