Integrals containing confluent hypergeometric functions with applications to perturbed singular potentials

Journal of Physics A: Mathematical and General

Volumn 36, Issue 28, 2003, Pages 7771-7788

  Saad, Nasser ^a   Hall, Richard L ^b  

^a UNIVERSITY OF PRINCE EDWARD ISLAND   (Canada)

^b Gina Cody School of Engineering and Computer Science   (Canada)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0038372942     PISSN: 03054470     EISSN: None     Source Type: Journal    
DOI: 10.1088/0305-4470/36/28/307     Document Type: Article

References (33)

1. Landau L D and Lifshitz E M 1981 Quantum Mechanics: Non-relativistic Theory (London: Pergamon) appendix f, p 662
2. Gordon W 1929 Ann. Phys., Lpz. 2 1031
3. Karule E 1990 J. Phys. A: Math. Gen. 23 1969-71
4. Sud Krishan and Wright L E 1979 J. Math. Phys. 17 1719-21
5. Nordsieck A 1954 Phys. Rev. 93 785-7
6. Gradshteyn I S and Ryzhik I M 2000 Tables of Integrals, Series, and Products 6th edn (New York: Academic) specifically 7.6
7. Appell P and Kampé de Férier J 1926 Fonctions Hypergéométriques et Hypérspheriques (Paris: Gauthier- Villars)
8. Slater L J 1966 Generalized Hypergeometric Functions (Cambridge: Cambridge University Press) ch 8
9. Srivastava H M and Manocha H L 1984 A Treatise on Generating Functions (New York: Halsted/Wiley)
10. Srivastava H M and Karlsson P W 1985 Multiple Gaussian Hypergeometric Series (New York: Halsted/ Wiley)
11. Erdélyi A 1936 Math. Z. 42 125
12. Erdélyi A, Magnus W, Oberhettinger F and Tricomi F G 1953 Higher Transcedental Functions (New York: McGraw-Hill) vol 1, p 278
13. Gargaro W W and Onley D S 1971 Phys. Rev. C 4 1032-43
14. Hahne G E 1969 J. Math. Phys. 10 524-31
15. Saad N and Hall R L 2002 J. Phys. A: Math. Gen. 35 4105-23
16. Slater L J 1966 Generalized Hypergeometric Functions (Cambridge: Cambridge University Press) p 214, formula (8.2.3)
17. Andrews G E, Askey R and Roy R 1999 Special Functions (Cambridge: Cambridge University Press) p 65, theorem 2.2.1
18. Andrews G E, Askey R and Roy R 1999 Special Functions (Cambridge: Cambridge University Press) p 68, theorem 2.2.5
19. Slater L J 1966 Generalized Hypergeometric Functions (Cambridge: Cambridge University Press) p 215, formula (8.2.5)
20. Slater L J 1966 Generalized Hypergeometric Functions (Cambridge: Cambridge University Press) p 218, formula (8.3.5)
21. Landau L D and Lifshitz EM 1981 Quantum Mechanics: Non-relativistic Theory (London: Pergamon) formula f.10, p 664
22. Cuyt A, Driver K, Tan J and Vertonk B 1999 J. Comp. Appl. Math. 5 213-9
23. Buchholz H 1969 The Confluent Hypergeometric Function (Berlin: Springer) formula (46) p 119
24. Buchholz H 1969 The Confluent Hypergeometric Function (Berlin: Springer) formula (4,β) p 119
25. Andrews G E, Askey R and Roy R 1999 Special Functions (Cambridge: Cambridge University Press) p 67, corollary 2.2.3
26. Glasser M L and Montaldi E 1993 Preprint math.CA/9307213V1
27. Hall R, Saad N and von Keviczky A 2001 J. Phys. A: Math. Gen. 34 1169-79
28. Hall R, Saad N and von Keviczky A 1998 J. Math. Phys. 39 6345-51
29. Hall R and Saad N 2000 J. Phys. A: Math. Gen. 33 569-78
30. Hall R and Saad N 2000 J. Phys. A: Math. Gen. 33 5531-7
31. Fernández Francisco M 1992 Phys. Rev. A 45 1333-8
32. Landau L D and Lifshitz E M 1981 Quantum Mechanics: Non-Relativistic Theory (London: Pergamon) problem 3, p 127
33. Magnus W, Oberhettinger F and Soni R P 1966 Formulas and Theorems for the Special Functions of Mathematical Physics (New York: Springer) ch 2