Generalized Bessel functions and Kapteyn series

Computers and Mathematics with Applications

Volumn 35, Issue 8, 1998, Pages 117-125

  Dattoli, G ^a   Torre, A ^a   Lorenzutta, S ^b   Maino, G ^b  

^a ENEA   (Italy)

^b Divisione Calcolo   (Italy)

Author keywords

Bessel functions; Eccentric anomaly; Kapteyn series; Kepler problem; True anomaly

Indexed keywords

ASTRONOMY; DIFFERENTIAL EQUATIONS; ELECTROMAGNETIC FIELD THEORY; INTEGRAL EQUATIONS; NUMBER THEORY;

BESSEL FUNCTION; ELECTROMAGNETIC RADIATION THEORY; KAPTEYN SERIES; KEPLER PROBLEM;

FUNCTIONS;

EID: 0032040791     PISSN: 08981221     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0898-1221(98)00050-9     Document Type: Article

References (14)

1. G.N. Watson, A Treatise on the Theory of Bessel Functions, Cambridge University Press, London, (1958).
2. A.F. Nikiforov and V.B. Uvarov, Special Functions of Mathematical Physics, Birkhauser, Basel, (1988).
3. E.D. Rainville, Special Functions, The MacMillan Company, New York, (1960).
4. R. Askey, Editor, Theory and Applications of Special Functions, Academic Press, New York, (1975).
5. P. Appell and J. Kampé de Fériét, Fonctions Hypérgeométriques et Hypersphériques. Polynomes d'Hermite, Gauthier-Villars, Paris, (1926).
6. M.B. Jekhowsky, Application des fonctions de Bessel a plusieues varialdes au movement elliptique, Bull. Astr. XXXV, 139 (1918).
7. L.S. Brown and T.W.B. Kibble, Interaction of intense laser beams with electrons, Phys. Rev. 133 (A705) (1964).
8. G. Dattoli, L. Giannessi, L. Mezi and A. Torre, Nuovo Cimento B105, 3217 (1990).
9. G. Dattoli, A. Torre, S. Lorenzutta, G. Maino and C. Chiccoli, Nuovo Cimento B106, 21 (1991).
10. W. Miller, Jr., On a generalization of Bessel functions, Comm. Pure Appl. Math. 18, 493 (1965).
11. W. Kapteyn, Recherches sur les fonctions de Fourier-Bessel, Ann. Sci. de l'Ecole Norm. Sup. X (3), 91-120 (1893).
12. H.C. Plummer, Dynamical Astronomy, Cambridge, (1918).
13. G. Dattoli and A. Torre, Theory and Applications of Generalized Bessel Functions, Aracne Editrice, Rome, (1996).
14. E.S. Sarachik and G.T. Schappert, Classical theory of the scattering of intense laser radiation by free electrons, Phys. Rev. D1, 2738 (1970).