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Volumn 25, Issue 2, 2007, Pages 181-186

On Turán's inequality for Legendre polynomials

Author keywords

Legendre polynomials; Normalized binomial mid coefficient; Tur n's inequality

Indexed keywords


EID: 33947721487     PISSN: 07230869     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.exmath.2006.11.001     Document Type: Article
Times cited : (19)

References (16)
  • 1
    • 84939593383 scopus 로고    scopus 로고
    • M. Abramowitz, I. Stegun (Eds.), Handbook of Mathematical Functions with Formulas and Mathematical Tables, Dover, New York, 1965.
  • 2
    • 28444454504 scopus 로고    scopus 로고
    • Normalized binomial mid-coefficients and power means
    • Alzer H., and Fuglede B. Normalized binomial mid-coefficients and power means. J. Number Theory 115 (2005) 284-294
    • (2005) J. Number Theory , vol.115 , pp. 284-294
    • Alzer, H.1    Fuglede, B.2
  • 4
    • 84939583215 scopus 로고    scopus 로고
    • Remembering Paul Turán
    • Askey R. Remembering Paul Turán. J. Approx. Theory 86 (1996) 253-254
    • (1996) J. Approx. Theory , vol.86 , pp. 253-254
    • Askey, R.1
  • 5
    • 38249016332 scopus 로고
    • No two quotients of normalized binomial mid-coefficients are equal
    • Bang T., and Fuglede B. No two quotients of normalized binomial mid-coefficients are equal. J. Number Theory 35 (1990) 345-349
    • (1990) J. Number Theory , vol.35 , pp. 345-349
    • Bang, T.1    Fuglede, B.2
  • 6
    • 51249171622 scopus 로고
    • Liouville's operator for a disc in space
    • Berg C., and Fuglede B. Liouville's operator for a disc in space. Manuscripta Math. 67 (1990) 165-185
    • (1990) Manuscripta Math. , vol.67 , pp. 165-185
    • Berg, C.1    Fuglede, B.2
  • 7
    • 27344448151 scopus 로고    scopus 로고
    • On the inequality of P. Turán for Legendre polynomials
    • 〈http://jipam.vu.edu.au/〉
    • Constantinescu E. On the inequality of P. Turán for Legendre polynomials. J. Inequal. Pure Appl. Math. 6 2 (2005) Art. 28. http://jipam.vu.edu.au/ 〈http://jipam.vu.edu.au/〉
    • (2005) J. Inequal. Pure Appl. Math. , vol.6 , Issue.2
    • Constantinescu, E.1
  • 8
    • 22044435255 scopus 로고    scopus 로고
    • Higher order Turán inequalities
    • Dimitrov D.K. Higher order Turán inequalities. Proc. Amer. Math. Soc. 126 (1998) 2033-2037
    • (1998) Proc. Amer. Math. Soc. , vol.126 , pp. 2033-2037
    • Dimitrov, D.K.1
  • 9
    • 84968476541 scopus 로고
    • An inequality of Turán type for Jacobi polynomials
    • Gasper G. An inequality of Turán type for Jacobi polynomials. Proc. Amer. Math. Soc. 32 (1972) 435-439
    • (1972) Proc. Amer. Math. Soc. , vol.32 , pp. 435-439
    • Gasper, G.1
  • 10
    • 33744740031 scopus 로고    scopus 로고
    • S. Gerhold, M. Kauers, A procedure for proving special function inequalities involving a discrete parameter, Proceedings of ISSAC '05, ACM Press, 2005, pp. 156-162.
  • 11
    • 33744738485 scopus 로고    scopus 로고
    • A computer proof of Turán's inequality
    • 〈http://jipam.vu.edu.au/〉
    • Gerhold S., and Kauers M. A computer proof of Turán's inequality. J. Inequal. Pure Appl. Math. 7 2 (2006) Art. 42. http://jipam.vu.edu.au/ 〈http://jipam.vu.edu.au/〉
    • (2006) J. Inequal. Pure Appl. Math. , vol.7 , Issue.2
    • Gerhold, S.1    Kauers, M.2
  • 13
    • 84939593385 scopus 로고    scopus 로고
    • G. Szegö, Orthogonal Polynomials, fourth ed., Colloquium Publications, vol. 23, American Mathematical Society, Rhode Island, 1975.
  • 14
    • 33947714239 scopus 로고    scopus 로고
    • Positivity of Turán determinants for orthogonal polynomials
    • Ross K.A., et al. (Ed), Birkhäuser, Boston-Basel-Berlin
    • Szwarc R. Positivity of Turán determinants for orthogonal polynomials. In: Ross K.A., et al. (Ed). Harmonic Analysis and Hypergroups (1998), Birkhäuser, Boston-Basel-Berlin 165-182
    • (1998) Harmonic Analysis and Hypergroups , pp. 165-182
    • Szwarc, R.1
  • 15
    • 0002599532 scopus 로고
    • On the zeros of the polynomials of Legendre
    • Turán P. On the zeros of the polynomials of Legendre. Časopis Pest. Mat. Fys. 75 (1950) 113-122
    • (1950) Časopis Pest. Mat. Fys. , vol.75 , pp. 113-122
    • Turán, P.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.