Open Access

On some Turán-type inequalities

Journal of Inequalities and Applications20062006:29828

DOI: 10.1155/JIA/2006/29828

Received: 14 September 2005

Accepted: 20 September 2005

Published: 20 April 2006


We prove Turán-type inequalities for some special functions by using a generalization of the Schwarz inequality.


Authors’ Affiliations

Department of Mathematics, Roma Tre University


  1. Csordas G, Norfolk TS, Varga RS: The Riemann hypothesis and the Turán inequalities. Transactions of the American Mathematical Society 1986,296(2):521–541.MATHMathSciNetGoogle Scholar
  2. Elbert Á, Laforgia A: Some monotonicity properties of the zeros of ultraspherical polynomials. Acta Mathematica Hungarica 1986,48(1–2):155–159. 10.1007/BF01949060MATHMathSciNetView ArticleGoogle Scholar
  3. Elbert Á, Laforgia A: Monotonicity results on the zeros of generalized Laguerre polynomials. Journal of Approximation Theory 1987,51(2):168–174. 10.1016/0021-9045(87)90031-1MATHMathSciNetView ArticleGoogle Scholar
  4. Gradshteyn IS, Ryzhik IM: Table of Integrals, Series, and Products. 6th edition. Academic Press, California; 2000:xlvii+1163.MATHGoogle Scholar
  5. Katkova OM: Multiple positivity and the Riemann zeta-function.
  6. Laforgia A: Sturm theory for certain classes of Sturm-Liouville equations and Turánians and Wronskians for the zeros of derivative of Bessel functions. Indagationes Mathematicae 1982,44(3):295–301.MATHMathSciNetView ArticleGoogle Scholar
  7. Laforgia A, Natalini P: Turán-type inequalities for some special functions. submitted submittedGoogle Scholar
  8. Lorch L: Turánians and Wronskians for the zeros of Bessel functions. SIAM Journal on Mathematical Analysis 1980,11(2):223–227. 10.1137/0511021MATHMathSciNetView ArticleGoogle Scholar
  9. Pólya G: Collected Papers. Vol. II: Location of Zeros, edited by R. P. Boas, Mathematicians of Our Time. Volume 8. The MIT Press, Massachusetts; 1974.Google Scholar
  10. Szegö G: Orthogonal Polynomials, Colloquium Publications. Volume 23. 4th edition. American Mathematical Society, Rhode Island; 1975:xiii+432.Google Scholar
  11. Titchmarsh EC: The Theory of the Riemann Zeta-Function. The Clarendon Press, Oxford; 1951:vi+346.MATHGoogle Scholar
  12. Turán P: On the zeros of the polynomials of Legendre. Časopis Pro Pěstování Matematiky 1950, 75: 113–122.MATHGoogle Scholar


© Laforgia and Natalini 2006

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