Turán type inequalities for modified Bessel functions

Bulletin of the Australian Mathematical Society

Volumn 82, Issue 2, 2010, Pages 254-264

  Baricz, Árpád ^a  

^a BABE BOLYAI UNIVERSITY   (Romania)

Author keywords

Bessel functions; modified Bessel functions; Turn type inequalities

Indexed keywords

EID: 77957245228     PISSN: 00049727     EISSN: 17551633     Source Type: Journal    
DOI: 10.1017/S000497271000002X     Document Type: Article

References (31)

1. M. Abramowitz and I. A. Stegun (eds), Handbook of Mathematical Functions with Formulas, Graphs and Mathematical Tables (Dover Publications, New York, 1965).
2. H. Alzer and G. Felder, A Turán-type inequality for the gamma function, J. Math. Anal. Appl. 350 (2009), 276-282.
3. H. Alzer, S. Gerhold, M. Kauers and A. Lupa̧s, On Turns inequality for Legendre polynomials, Expo. Math. 25 (2007), 181-186.
4. D. E. Amos, Computation of modified Bessel functions and their ratios, Math. Comp. 28 (1974), 239-251.
5. Á. Baricz, Turán type inequalities for generalized complete elliptic integrals, Math. Z. 256(4) (2007), 895-911.
6. Á. Baricz, Functional inequalities involving Bessel and modified Bessel functions of the first kind, Expo. Math. 26(3) (2008), 279-293.
7. Á. Baricz, Turán type inequalities for hypergeometric functions, Proc. Amer. Math. Soc. 136(9) (2008), 3223-3229.
8. Á. Baricz, Mills ratio: monotonicity patterns and functional inequalities, J. Math. Anal. Appl. 340(2) (2008), 1362-1370.
9. Á. Baricz, On a product of modified Bessel functions, Proc. Amer. Math. Soc. 137(1) (2009), 189-193.
10. Á. Baricz, Turán type inequalities for some probability density functions, Studia Sci. Math. Hungar., in press.
11. R. W. Barnard, M. B. Gordy and K. C. Richards, A note on Turán type and mean inequalities for the Kummer function, J. Math. Anal. Appl. 349(1) (2009), 259-263.
12. T. H. Gronwall, An inequality for the Bessel functions of the first kind with imaginary argument, Ann. of Math. (2) 33(2) (1932), 275-278.
13. E. Grosswald, The Student t-distribution of any degree of freedom is infinitely divisible, Z. Wahrscheinlichkeitstheorie verw. Gebiete 36(2) (1976), 103-109.
14. M. E. H. Ismail, Bessel functions and the infinite divisibility of the Student t-distribution, Ann. Probab. 5(4) (1977), 582-585.
15. M. E. H. Ismail and A. Laforgia, Monotonicity properties of determinants of special functions, Constr. Approx. 26 (2007), 1-9.
16. M. E. H. Ismail and M. E. Muldoon, Monotonicity of the zeros of a cross-product of Bessel functions, SIAM J. Math. Anal. 9(4) (1978), 759-767.
17. C. M. Joshi and S. K. Bissu, Some inequalities of Bessel and modified Bessel functions, J. Aust. Math. Soc. Ser. A 50 (1991), 333-342.
18. A. Laforgia and P. Natalini, On some Turán-type inequalities, J. Inequal. Appl. 2006 (2006), 6, Article 29828.
19. L. Lorch, Monotonicity of the zeros of a cross product of Bessel functions, Methods Appl. Anal. 1(1) (1994), 75-80.
20. R. J. McEliece, B. Reznick and J. B. Shearer, A Turán inequality arising in information theory, SIAM J. Math. Anal. 12(6) (1981), 931-934.
21. B. N. Mukherjee and T. S. Nanjundiah, On an inequality relating to Laguerre and Hermite polynomials, Math. Student 19 (1951), 47-48.
22. M. E. Muldoon, Convexity properties of special functions and their zeros, in: Recent Progress in Inequalities, Math. Appl., 430 (ed. G. V. Milovanovic) (Kluwer Academic Publishers, Dordrecht, 1998), pp. 309-323.
23. R. Penfold, J.-M. Vanden-Broeck and S. Grandison, Monotonicity of some modified Bessel function products, Integral Transforms Spec. Funct. 18(2) (2007), 139-144.
24. R. S. Phillips and H. Malin, Bessel function approximations, Amer. J. Math. 72 (1950), 407-418.
25. H. Skovgaard, On inequalities of the Turán type, Math. Scand. 2 (1954), 65-73.
26. Y. Sun and Á. Baricz, Inequalities for the generalized Marcum Q-function, Appl. Math. Comput. 203(1) (2008), 134-141.
27. O. Szász, Inequalities concerning ultraspherical polynomials and Bessel functions, Proc. Amer. Math. Soc. 1 (1950), 256-267.
28. O. Szász, Identities and inequalities concerning orthogonal polynomials and Bessel functions, J. Anal. Math. 1 (1951), 116-134.
29. G. Szegõ, On an inequality of P. Turán concerning Legendre polynomials, Bull. Amer. Math. Soc. 54 (1948), 401-405.
30. V. K. Thiruvenkatachar and T. S. Nanjundiah, Inequalities concerning Bessel functions and orthogonal polynomials, Proc. Indian Nat. Acad. Part A 33 (1951), 373-384.
31. P. Turán, On the zeros of the polynomials of Legendre, Časopis Pest. Mat. Fys. 75 (1950), 113-122.