Operational Rules and Arbitrary Order Hermite Generating Functions

Journal of Mathematical Analysis and Applications

Volumn 227, Issue 1, 1998, Pages 98-111

  Dattoli, G ^a   Torre, A ^a   Carpanese, M ^a  

^a ENEA   (Italy)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0002528694     PISSN: 0022247X     EISSN: None     Source Type: Journal    
DOI: 10.1006/jmaa.1998.6080     Document Type: Article

References (13)

1. Nieto M. M., Truax D. Rodney. Arbitrary-order Hermite generating functions for obtaining arbitrary-order coherent and squeezed states. Phys. Lett. A208:1995;8-16.
2. Dattoli G., Torre A., Ottaviani P. L., Vázquez L. Evolution operator equations: Integration with algebraic and finite-difference methods. Applications to physical problems in classical and quantum mechanics and quantum field theory. Riv. Nuovo Cimento. 20:1997.
3. Crofton M. W. Theorems in the calculus of operations. Quart. J. Math. 16:1879;323-329.
4. Burchnall J. L. A note on the polynomials of Hermite. Quart. J. Math. Oxford Ser. (2). 1941;9-11.
5. Straneo S. L. Applicazione del metodo funzionale allo studio del raffreddamento di una sbarra. Rend. Accad. Lincei Roma. 8:1928;575-579.
6. Gould H. W., Hopper A. T. Operatorial formulas corrected with two generalizations of Hermite polynomials. Duke Math. J. 29:1962;51-63.
7. Dattoli G., Torre A. Theory and Applications of Generalized Bessel Functions. 1996;Aracne, Rome.
8. Rainville E. D. Special Functions. 1960;McMillan, New York.
9. Appell P., Kampé de Fériet J. Functions hypergeómétrique et hypersphériques. Polynomes d'Hermite. 1926;Gauthier-Villars, Paris.
10. Louck J. Extension of the Kibble-Slepian formula for Hermite polynomials using boson operator methods. Adv. in Appl. Math. 2:1981;239-249.
11. Erdélyi A. Higher Transcendental Functions. 1953;McGraw-Hill, New York. p. 194.
12. Srivastava H. M., Manocha H. L. A Treatise on Generating Functions. 1984;Ellis Horwood, New York. p. 496.
13. Srivastava H. M., Lavoie J.-L. A certain method of obtaining bilateral generating functions. Nederl. Akad. Wetensch. Proc. Ser. A78 Indag. Math. 37:1975;304-320.