Some inequalities of the Turán type for confluent hypergeometric functions of the second kind
DOI:
https://doi.org/10.24193/subbmath.2019.1.06Keywords:
Inequality of the Turán type, confluent hypergeometric function of the second kind, improvement, Mellin transform, Laplace transform, Hölder integral inequality.Abstract
In the paper, by virtue of the H¨older integral inequality, the authors derive some inequalities of the Turán type for confluent hypergeometric functions of the second kind, for the Mellin transforms, and for the Laplace transforms, and improve some known inequalities of the Turán type.
Mathematics Subject Classification (2010): 26D15, 26D20, 26D99, 33C15, 44A10, 44A15.
References
Abramowitz, M., Stegun, I.A. (eds.), Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, National Bureau of Standards, Applied Mathe- matics Series, 55, 10th printing, Washington, 1972.
Baricz, A´ ., Tur´an type inequalities for hypergeometric functions, Proc. Am. Math. Soc., 136(2008), no. 9, 3223-3229; Available online at https://doi.org/10.1090/S0002-9939-08-09353-2.
Baricz, A´ ., Tur´an type inequalities for modified Bessel functions, Bull. Aust. Math. Soc., 82(2010), no. 2, 254-264; Available online at https://doi.org/10.1017/S000497271000002X.
Baricz, A´ ., Ismail, M.E.H., Tur´an type inequalities for Tricomi confluent hypergeometric functions, Constr. Approx., 37(2013), no. 2, 195-221; Available online at https://doi.org/10.1007/s00365-012-9171-1.
Baricz, A´ ., Poga´ny, T.K., Tur´an determinants of Bessel functions, Forum Math., 26(2014), no. 1, 295-322; Available online at https://doi.org/10.1515/form.2011.160.
Baricz, A´ ., Ponnusamy, S., On Tura´n type inequalities for modified Bessel functions, Proc. Amer. Math. Soc., 141(2013), no. 2, 523-532; Available online at https://doi.org/10.1090/S0002-9939-2012-11325-5.
Baricz, A´ ., Ponnusamy, S., Singh, S., Tur´an type inequalities for confluent hypergeometric function of second kind, Studia Sci. Math. Hungar., 53(2016), no. 1, 74-92; Available online at https://doi.org/10.1556/012.2016.53.1.1330.
Bhukya, R., Akavaram, V., Qi, F., Some inequalities of the Tur´an type for confluent hypergeometric functions of the second kind, HAL archives (2018); Available online at https://hal.archives-ouvertes.fr/hal-01701854.
Gradshteyn, I.S., Ryzhik, I.M., Table of Integrals, Series, and Products, Translated from the Russian, Translation Edited and With a Preface by Daniel Zwillinger and Victor Moll, Eighth Edition, Revised from the Seventh Edition, Elsevier/Academic Press, Amsterdam, 2015; Available online at https://doi.org/10.1016/B978-0-12-384933-5.00013-8.
Erd´elyi, A., Magnus, W., Oberhettinger, F., Tricomi, F.G., Tables of Integral Transforms, Vol. I, McGraw-Hill Book Company, Inc., New York-Toronto-London, 1954.
Laforgia, A., Natalini, P., Tur´an type inequalities for some special functions, J. Inequal. Pure Appl. Math., 7(2006), no. 1, Art. 22; Available online at http://www.emis.de/journals/JIPAM/article638.html.
Qi, F., Bhukya, R., Akavaram, V., Inequalities of the Gru¨nbaum type for completely monotonic functions, Adv. Appl. Math. Sci., 17(2018), no. 3, 331-339.
Qi, F., Guo, B.-N., Complete monotonicity of the divided differences of di- and trigamma functions and its applications, Georgian Math. J., 23(2016), no. 2, 279-291; Available online at http://dx.doi.org/10.1515/gmj-2016-0004.
Qi, F., Guo, B.-N., Integral representations and complete monotonicity of remainders of the Binet and Stirling formulas for the gamma function, Rev. R. Acad. Cienc. Exactas F´ıs. Nat. Ser. A Math. RACSAM, 111 (2017), no. 2, 425-434; Available online at https://doi.org/10.1007/s13398-016-0302-6.
Qi, F., Li, W.-H., A logarithmically completely monotonic function involving the ratio of gamma functions, J. Appl. Anal. Comput., 5(2015), no. 4, 626-634; Available online at http://dx.doi.org/10.11948/2015049.
Tura´n, P., On the zeros of the polynomials of Legendre, Cˇ asopis Pˇest. Mat. Fys., 75(1950), 113-122.
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2019 Studia Universitatis Babeș-Bolyai Mathematica
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.
