Evaluation of integrals involving orthogonal polynomials: Laguerre polynomial and Bessel function example

Applied Mathematics Letters

Volumn 20, Issue 1, 2007, Pages 38-42

  Alhaidari, A D ^a,b  

^a Shura Council   (Saudi Arabia)

^b KING FAHD UNIVERSITY OF PETROLEUM AND MINERALS   (Saudi Arabia)

Author keywords

Associated Laguerre polynomial; Bessel function; Definite integrals; Function spectral decomposition; Gegenbauer polynomial; Recursion relation

Indexed keywords

ASSOCIATED LAGUERRE POLYNOMIALS; DEFINITE INTEGRALS; FUNCTION SPECTRAL DECOMPOSITION; GEGENBAUER POLYNOMIALS; RECURSION RELATIONS;

BESSEL FUNCTIONS; INTEGRAL EQUATIONS; RECURSIVE FUNCTIONS; SPECTRUM ANALYSIS;

POLYNOMIALS;

EID: 33750026703     PISSN: 08939659     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.aml.2006.02.020     Document Type: Article

References (22)

1. Morse P.M., and Feshbach H. Methods of Theoretical Physics vol. I (1953), McGraw-Hill, New York
2. Courant R., and Hilbert D. Methods of Mathematical Physics vol. I (1966), Interscience, New York
3. Arfken G. Mathematical Methods for Physicists. 2nd ed. (1970), Academic, New York pp. 478-533
4. Messiah A. Quantum Mechanics vol. I (1965), North-Holland, Amsterdam
5. Merzbacher E. Quantum Mechanics. 2nd ed. (1970), Wiley, New York
6. Liboff R.L. Quantum Mechanics. 2nd ed. (1992), Addison-Wesley, Reading
7. See, for example. Gradshteyn I.S., and Ryzhik I.M. Tables of Integrals, Series, and Products (1980), Academic, New York
8. Newton R.G. Scattering Theory of Waves and Particles. 2nd ed. (1966), Springer, New York
9. Gelman S. Topics in Atomic Collision Theory (1969), Academic, New York
10. Bransden B.H. Atomic Collision Theory (1970), Benjamin, New York
11. Taylor J.R. Scattering Theory (1972), Wiley, New York
12. Burke P.G. Potential Scattering in Atomic Physics (1977), Plenum, New York
13. Heller E.J., and Yamani H.A. Phys. Rev. A 9 (1974) 1201
14. Yamani H.A., and Fishman L. J. Math. Phys. 16 (1975) 410
15. In: Alhaidari A.D., Heller E.J., Yamani H.A., and Abdelmonem M.S. (Eds). The J-matrix method: Recent Developments and Selected Applications (2006), Springer, Amsterdam
16. In: Erdélyi A. (Ed). Higher Transcendental Functions vol. I (1953), McGraw-Hil1, New York
17. In: Abramowitz M., and Stegun I.A. (Eds). Handbook of Mathematical Functions (1965), Dover, New York
18. Chihara T.S. An Introduction to Orthogonal Polynomials (1978), Gordon and Breach, New York
19. Szegö G. Orthogonal polynomials. 4th ed. (1997), Am. Math. Soc., Providence, RI
20. Magnus W., Oberhettinger F., and Soni R.P. Formulas and Theorems for the Special Functions of Mathematical Physics. 3rd ed. (1966), Springer, New York p. 242
21. Page 91 of Ref. [7]
22. Page 222 of Ref. [7]