메뉴 건너뛰기




Volumn 36, Issue 17, 2003, Pages 4857-4865

Information entropy of Gegenbauer polynomials and Gaussian quadrature

Author keywords

[No Author keywords available]

Indexed keywords


EID: 0242298274     PISSN: 03054470     EISSN: None     Source Type: Journal    
DOI: 10.1088/0305-4470/36/17/312     Document Type: Article
Times cited : (12)

References (18)
  • 1
    • 84856043672 scopus 로고
    • A mathematical theory of communication
    • Shannon C E 1948 A mathematical theory of communication Bell Syst. Tech. J. 27 379-423, 623-56 Reprinted in Shannon C E and Weaver W (ed) 1949 The Mathematical Theory of Communication (Urbana, IL: University of Illinois Press)
    • (1948) Bell Syst. Tech. J. , vol.27 , pp. 379-423
    • Shannon, C.E.1
  • 2
    • 84940644968 scopus 로고
    • Urbana, IL: University of Illinois Press
    • Shannon C E 1948 A mathematical theory of communication Bell Syst. Tech. J. 27 379-423, 623-56 Reprinted in Shannon C E and Weaver W (ed) 1949 The Mathematical Theory of Communication (Urbana, IL: University of Illinois Press)
    • (1949) The Mathematical Theory of Communication
    • Shannon, C.E.1    Weaver, W.2
  • 3
    • 0000898117 scopus 로고
    • Inequalities in Fourier analysis
    • Beckner W 1975 Inequalities in Fourier analysis Am. Math. 102 159-82 Bialynicki-Birula I and Mycielski J 1975 Uncertainty relations for information entropy in wave mechanics Commun. Math. Phys. 44 129-32
    • (1975) Ann. Math. , vol.102 , pp. 159-182
    • Beckner, W.1
  • 4
    • 0000617016 scopus 로고
    • Uncertainty relations for information entropy in wave mechanics
    • Beckner W 1975 Inequalities in Fourier analysis Am. Math. 102 159-82 Bialynicki-Birula I and Mycielski J 1975 Uncertainty relations for information entropy in wave mechanics Commun. Math. Phys. 44 129-32
    • (1975) Commun. Math. Phys. , vol.44 , pp. 129-132
    • Bialynicki-Birula, I.1    Mycielski, J.2
  • 6
    • 34547109818 scopus 로고
    • Position and momentum information entropies of the D- dimensional harmonic oscillator and hydrogen atom
    • Yáñez R J, Van Assche W and Dehesa J S 1994 Position and momentum information entropies of the D- dimensional harmonic oscillator and hydrogen atom Phys. Rev. A 50 3065-79
    • (1994) Phys. Rev. A , vol.50 , pp. 3065-3079
    • Yáñez, R.J.1    Van Assche, W.2    Dehesa, J.S.3
  • 7
    • 0002406120 scopus 로고    scopus 로고
    • Information entropy of classical orthogonal polynomials and their application to the harmonic oscillator and Coulomb potentials
    • Dehesa J S, Van Assche W and Yáñez R J 1997 Information entropy of classical orthogonal polynomials and their application to the harmonic oscillator and Coulomb potentials Meth. Appl. Anal. 4 91-110
    • (1997) Meth. Appl. Anal. , vol.4 , pp. 91-110
    • Dehesa, J.S.1    Van Assche, W.2    Yáñez, R.J.3
  • 8
    • 0033228877 scopus 로고    scopus 로고
    • Entropic integrals of hyperspherical harmonics and spatial entropy of D-dimensional central potentials
    • Yáñez R J, Van Assche W, González-Férez R and Dehesa J S 1999 Entropic integrals of hyperspherical harmonics and spatial entropy of D-dimensional central potentials J. Math. Phys. 40 5675-86
    • (1999) J. Math. Phys. , vol.40 , pp. 5675-5686
    • Yáñez, R.J.1    Van Assche, W.2    González-Férez, R.3    Dehesa, J.S.4
  • 10
    • 0002441861 scopus 로고    scopus 로고
    • On information entropy of Gegenbauer polynomials
    • in Russian
    • Buyarov V S 1997 On information entropy of Gegenbauer polynomials Vestn. Mosk. Univ. Ser. I Mat. Mekh. 6 8-11 (in Russian)
    • (1997) Vestn. Mosk. Univ. Ser. I Mat. Mekh. , vol.6 , pp. 8-11
    • Buyarov, V.S.1
  • 12
    • 84966223722 scopus 로고
    • On estimates for the weights in Gaussian quadrature in the ultraspherical case
    • Förster K-J and Petras K 1990 On estimates for the weights in Gaussian quadrature in the ultraspherical case Math. Comput. 55 243-64
    • (1990) Math. Comput. , vol.55 , pp. 243-264
    • Förster, K.-J.1    Petras, K.2
  • 13
    • 0030545275 scopus 로고    scopus 로고
    • An asymptotic expansion for the weights of Gaussian quadrature formulae
    • Petras K 1996 An asymptotic expansion for the weights of Gaussian quadrature formulae Acta Math. Hung. 70 89-100
    • (1996) Acta Math. Hung. , vol.70 , pp. 89-100
    • Petras, K.1
  • 15
    • 21844515666 scopus 로고
    • Spatial entropy of central potentials and strong asymptotics of orthogonal polynomials
    • p-norms and entropy for general orthogonal polynomials Russ. Acad. Sci. Sb. Math. 82 373-95 Aptekarev A I, Buyarov V S, Van Assche W and Dehesa J S 1996 Asymptotics of entropy integrals for orthogonal polynomials Dokl. Math. 53 47-9
    • (1994) J. Math. Phys. , vol.35 , pp. 4423-4428
    • Aptekarev, A.I.1    Dehesa, J.S.2    Yáñez, R.J.3
  • 16
    • 0000204517 scopus 로고
    • p-norms and entropy for general orthogonal polynomials
    • p-norms and entropy for general orthogonal polynomials Russ. Acad. Sci. Sb. Math. 82 373-95 Aptekarev A I, Buyarov V S, Van Assche W and Dehesa J S 1996 Asymptotics of entropy integrals for orthogonal polynomials Dokl. Math. 53 47-9
    • (1995) Russ. Acad. Sci. Sb. Math. , vol.82 , pp. 373-395
    • Aptekarev, A.I.1    Buyarov, V.S.2    Dehesa, J.S.3
  • 17
    • 0003922665 scopus 로고    scopus 로고
    • Asymptotics of entropy integrals for orthogonal polynomials
    • p-norms and entropy for general orthogonal polynomials Russ. Acad. Sci. Sb. Math. 82 373-95 Aptekarev A I, Buyarov V S, Van Assche W and Dehesa J S 1996 Asymptotics of entropy integrals for orthogonal polynomials Dokl. Math. 53 47-9
    • (1996) Dokl. Math. , vol.53 , pp. 47-49
    • Aptekarev, A.I.1    Buyarov, V.S.2    Van Assche, W.3    Dehesa, J.S.4
  • 18
    • 0037095342 scopus 로고    scopus 로고
    • On the asymptotic expansion of the entropy of Gegenbauer polynomials
    • Sánchez-Lara J F 2002 On the asymptotic expansion of the entropy of Gegenbauer polynomials J. Comput. Appl. Math. 142 401-9
    • (2002) J. Comput. Appl. Math. , vol.142 , pp. 401-409
    • Sánchez-Lara, J.F.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.