Entropic integrals of orthogonal hypergeometric polynomials with general supports

Journal of Computational and Applied Mathematics

Volumn 118, Issue 1-2, 2000, Pages 311-322

  Sánchez Ruiz, Jorge ^a,b   Dehesa, Jesús S ^b  

^a UNIVERSIDAD CARLOS III DE MADRID   (Spain)

^b UNIVERSITY OF GRANADA   (Spain)

Author keywords

Entropy like integrals; Hypergeometric polynomials; Information entropy; Probability measures; Second order differential equations

Indexed keywords

EID: 17444442111     PISSN: 03770427     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0377-0427(00)00296-X     Document Type: Article

References (29)

1. Aptekarev A.I., Dehesa J.S., Yáñez R.J. Spatial entropy of central potentials and strong asymptotics of orthogonal polynomials. J. Math. Phys. 35:1994;4423-4428.
2. p -norms and entropy for general orthogonal polynomials Russian Acad. Sci. Sb. Math. 82:1995;373-395.
3. Aptekarev A.I., Buyarov V.S., Van Assche W., Dehesa J.S. Asymptotics of entropy integrals for orthogonal polynomials. Dokl. Math. 53:1996;47-49.
4. Artés P.L., Dehesa J.S., Martínez-Finkelshtein A., Sánchez-Ruiz J. Linearization and connection coefficients for hypergeometric-type polynomials. J. Comput. Appl. Math. 99:1998;15-26.
5. Avery J. Hyperspherical Harmonics, Applications to Quantum Theory. 1989;Kluwer, Dordrecht.
6. Bagrov V.G., Gitman D.M. Exact Solutions of Relativistic Wave Equations. 1990;Kluwer, Dordrecht.
7. Budzinski J. Evaluation of two-center, two- and three-electron integrals involving correlation factors over Slater-type orbitals. II. Kinetic and potential energy integrals and examples of numerical results. Internat. J. Quantum Chem. 41:1992;359-370.
8. V.S. Buyarov, On information entropy of Gegenbauer polynomials, Vesnt. Mosk. Univ. (Ser. 1) 6 (1997) 8-11 (in Russian).
9. V.S. Buyarov, P. López-Artés, A. Martínez-Finkelshtein, W. Van Assche, Information entropy of Gegenbauer polynomials, preprint, 2000.
10. Dehesa J.S., Domínguez Adame F., Arriola E.R., Zarzo A. Hydrogen atom and orthogonal polynomials. Brezinski C., Gori L., Ronveaux A. Orthogonal Applications and their Applications. 1991;223-229 Baltzer, Ginebra.
11. Dehesa J.S., Yáñez R.J., Pérez-Victoria M., Sarsa A. Orthogonal polynomials and their applications. J. Math. Anal. Appl. 188:1994;35-43.
12. Dehesa J.S., Van Assche W., Yáñez R.J. Information entropy of classical orthogonal polynomials and their application to the harmonic oscillator and Coulomb potentials. Meth. Appl. Anal. 4:1997;91-110.
13. Dehesa J.S., Yáñez R.J., Aptekarev A.I., Buyarov V.S. Strong asymptotics of Laguerre polynomials and information entropies of two-dimensional harmonic oscillator and one-dimensional Coulomb potentials. J. Math. Phys. 39:1998;3050-3060.
14. J.S. Dehesa, A. Martínez-Finkelshtein, J. Sánchez-Ruiz, Quantum information entropies and orthogonal polynomials, J. Comput. Appl. Math., to be published.
15. Erdélyi (Ed.) A. Higher Transcendental Functions, Vol. II. 1953;McGraw-Hill, New York.
16. Hobson E.W. The Theory of Spherical and Ellipsoidal Harmonics. 1968;Chelsea, New York.
17. Nikiforov A.F., Uvarov V.B. Special Functions in Mathematical Physics. 1988;Birkhaüser, Basel.
18. Sánchez-Ruiz J. Logarithmic potential of Hermite polynomials and information entropies of the harmonic oscillator eigenstates. J. Math. Phys. 38:1997;5031-5043.
19. Sánchez-Ruiz J., Dehesa J.S. Expansions in series of orthogonal hypergeometric polynomials. J. Comput. Appl. Math. 89:1998;155-170.
20. C.E. Shannon, A mathematical theory of communication, Bell Syst. Tech. J. 27 (1948) 379-423, 623-656; reprinted in: C.E. Shannon, W. Weaver (Eds.), The Mathematical Theory of Communication, University of Illinois Press, Urbana, IL, 1949.
21. C.E. Shannon, A mathematical theory of communication, Bell Syst. Tech. J. 27 (1948) 379-423, 623-656; reprinted in: C.E. Shannon, W. Weaver (Eds.), The Mathematical Theory of Communication, University of Illinois Press, Urbana, IL, 1949.
22. Van Assche W., Yáñez R.J., Dehesa J.S. Entropy of orthogonal polynomials with Freud weights and information entropies of the harmonic oscillator potential. J. Math. Phys. 36:1995;4106-4118.
23. W. Van Assche, R.J. Yáñez, R. González-Férez, J.S. Dehesa, Functionals of Gegenbauer polynomials and D -dimensional hydrogenic momentum expectation values, J. Math. Phys., 2000, submitted for publication.
24. Vilenkin N.Ja., Klymik A.U. Representations of Lie Groups and Special Functions, Vol. II. 1993;Kluwer, Dordrecht.
25. Yáñez R.J., Dehesa J.S., Nikiforov A.F. The three-term recurrence relation and the differentiation formulas for hypergeometric type functions. J. Math. Anal. Appl. 188:1994;855-866.
26. Yáñez R.J., Van Assche W., Dehesa J.S. Position and momentum information entropies of the. D -dimensional harmonic oscillator and hydrogen atom Phys. Rev. A. 50:1994;3065-3079.
27. R.J. Yáñez, Information entropy, orthogonal polynomials and many-electron systems, Ph.D. Thesis, University of Granada, 1996 (in Spanish).
28. Yáñez R.J., Van Assche W., González-Férez R., Dehesa J.S. Entropic integrals of hyperspherical harmonics and spatial entropy of. D -dimensional central potentials J. Math. Phys. 40:1999;5675-5686.
29. Znojil M. Jacobi polynomials and bound states. J. Math. Chem. 19:1996;205-213.