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Original Articles

Van der Corput inequalities for Bessel functions

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Pages 78-87 | Received 22 Aug 2014, Accepted 07 Oct 2014, Published online: 28 Oct 2014

References

  • Watson GN. A treatise on the theory of Bessel functions. Cambridge: Cambridge University Press; 1944.
  • Neuman E. Inequalities involving modified Bessel functions of the first kind. J Math Anal Appl. 1992;171:532–536. doi: 10.1016/0022-247X(92)90363-I
  • Baricz Á, Neuman E. Inequalities involving modified Bessel functions of the first kind II. J Math Anal Appl. 2007;332:265–271. doi: 10.1016/j.jmaa.2006.10.007
  • Giordano C, Laforgia A, Pečarić J. Supplement to known inequalities for some special functions. J Math Anal Appl. 1996;200:34–41. doi: 10.1006/jmaa.1996.0188
  • Ismail MEH. Remarks on a paper by Giordano, Laforgia, and Pearić. J Math Anal Appl. 1997;211:621–625. doi: 10.1006/jmaa.1997.5391
  • Baricz Á.  Generalized Bessel functions of the first kind [PhD thesis]. Cluj-Napoca: Babeş-Bolyai University; 2008.
  • Baricz Á.  Generalized Bessel functions of the first kind. Vol. 1994, Lecture Notes in Mathematics. Berlin: Springer; 2010.
  • Mitrinović DS. Analytic inequalities. Berlin: Springer-Verlag; 1970.
  • Yuan L, Kalbfleisch JD. On the Bessel distribution and related problems. Ann Inst Statist Math. 2000;52:438–447. doi: 10.1023/A:1004152916478
  • Segura J. Bounds for ratios of modified Bessel functions and associated Turán-type inequalities. J Math Anal Appl. 2011;374:516–528. doi: 10.1016/j.jmaa.2010.09.030
  • Amos DE. Computation of modified Bessel functions and their ratios. Math Comp. 1974;28:239–251. doi: 10.1090/S0025-5718-1974-0333287-7
  • Gronwall TH. An inequality for the Bessel functions of the first kind with imaginary argument. Ann Math. 1932;33:275–278. doi: 10.2307/1968329
  • van der Corput JG. Problem 95. Wisk Opgaven. 1935;16:242–243.
  • Ismail MEH, Muldoon ME. Monotonicity of the zeros of a cross-product of Bessel functions. SIAM J Math Anal. 1978;9:759–767. doi: 10.1137/0509055
  • Baricz Á. Functional inequalities involving Bessel and modified Bessel functions of the first kind. Expo Math. 2008;26:279–293. doi: 10.1016/j.exmath.2008.01.001
  • Baricz Á. Geometrically concave univariate distributions. J Math Anal Appl. 2010;363:182–196. doi: 10.1016/j.jmaa.2009.08.029

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