참고문헌
- M. Abramowitz and I. A. Stegun (eds), Handbook of Mathematical Functions with Formulas, Graphs and Mathematical Tables, Dover Publications, New York, 1965.
- G. D. Anderson, S.-L. Qiu, M. K. Vamanamurthy, and M. Vuorinen, Generalized elliptic integral and modular equations, Pacific J. Math. 192 (2000), 1-7. https://doi.org/10.2140/pjm.2000.192.1
- A. Baricz, Functional inequalities involving Bessel and modied Bessel functions of the rst kind, Expo. Math. 26 (2008), no. 3, 279-293. https://doi.org/10.1016/j.exmath.2008.01.001
- A. Baricz, Bounds for modied Bessel functions of the rst and second kinds, Proc. Edinb. Math. Soc. (2) 53 (2010), no. 3, 575-599. https://doi.org/10.1017/S0013091508001016
- A. Erdelyi, W. Magnus, F. Oberhettinger, and F. Tricomi, Higher transcendental Functions, vol. 2, McGraw-Hill, New York, 1954.
- C. Huygens, Oeuvres completes, publiees par la Societe hollandaise des science, Haga, 1888-1940 (20 volumes).
- K. Mehrez, Redheer type inequalities for modied Bessel functions, Arab J. Math. Sci. 22 (2016), no. 1, 38-42. https://doi.org/10.1016/j.ajmsc.2015.03.001
- K. Mehrez, Functional inequalities for the Wright functions, Integral Transforms Spec. Funct. 28 (2017), no. 2, 130-144. https://doi.org/10.1080/10652469.2016.1254628
- K. Mehrez and S. M. Sitnik, On monotonicity of ratios of some q-hypergeometric functions, Mat. Vesnik 68 (2016), no. 3, 225-231.
- K. Mehrez and S. M. Sitnik, Functional inequalities for the Mittag-Leer functions, Results Math. 72 (2017), no. 1-2, 703-714. https://doi.org/10.1007/s00025-017-0664-x
- E. Neuman and J. Sandor, On some inequalities involving trigonometric and hyperbolic functions with emphasis on the Cusa-Huygens, Wilker, and Huygens inequalities, Math. Inequal. Appl. 13 (2010), no. 4, 715-723. https://doi.org/10.7153/mia-13-50
- K. S. Nisar, S. R. Mondal, and J. Choi, Certain inequalities involving the k-Struve function, J. Inequal. Appl. 2017 (2017), Paper No. 71, 8 pp. https://doi.org/10.1186/s13660-017-1343-x
- I. Pinelis, "Non-strict" l'Hospital-type rules for monotonicity: intervals of constancy, JIPAM. J. Inequal. Pure Appl. Math. 8 (2007), no. 1, Article 14, 8 pp.
- S. Ponnusamy and M. Vuorinen, Asymptotic expansions and inequalities for hypergeometric functions, Mathematika 44 (1997), no. 2, 278-301. https://doi.org/10.1112/S0025579300012602
- K. A. Selvakumaran, H. A. AL-Kharshani, D. Baleanu, S. D. Purohit, and K. S. Nisar, Inclusion relationships for some subclasses of analytic functions associated with generalized Bessel functions, J. Comput. Anal. Appl. 24 (2018), no. 1, 81-90. https://doi.org/10.1515/jaa-2018-0008
- S. M. Sitnik and Kh. Mekhrez, Monotonicity of the ratios of some hypergeometric functions, Sib. Elektron. Mat. Izv. 13 (2016), 260-268.
- S. M. Sitnik and Kh. Mekhrez, Proofs of some conjectures on monotonicity of ratios of Kummer, Gauss and generalized hypergeometric functions, Analysis (Berlin) 36 (2016), no. 4, 263-268. https://doi.org/10.1515/anly-2015-0029
- G. N. Watson, A Treatise on the Theory of Bessel Functions, Cambridge University Press, Cambridge, England, 1944.
- L. Zhu, Some new inequalities of the Huygens type, Comput. Math. Appl. 58 (2009), no. 6, 1180-1182. https://doi.org/10.1016/j.camwa.2009.07.045