EXTENSION OF FRAME'S TYPE INEQUALITIES TO BESSEL AND MODIFIED BESSEL FUNCTIONS
0
조회
0
다운로드
0
인용
0
참고문헌
키워드
초록
Our aim is to extend some trigonometric inequalities to Bessel functions. Moreover, we extend the hyperbolic analogue of these trigonometric inequalities. As an application of these results we present a generalization of Cusa-type inequality to modi ed Bessel function. Our main motivation to write this paper is a recent publication of Chen and Sandor, which we wish to complement.
Abstract
Our aim is to extend some trigonometric inequalities to Bessel functions. Moreover, we extend the hyperbolic analogue of these trigonometric inequalities. As an application of these results we present a generalization of Cusa-type inequality to modi ed Bessel function. Our main motivation to write this paper is a recent publication of Chen and Sandor, which we wish to complement.
참고문헌 (10)
- M. Abramowitz, "Handbook of Mathematical Functions with Formulas, Graphs and Mathematical Tables" (1965), Dover Publications
- C.-P. CHen, "Sharp inequalities for trigonometric and hyperbolic functions", J. Math. Ineq, 9(1), pp.203~217 (2015)
- J. S. Frame, "Some trigonometric, hyperbolic and elliptic approximations", Amer. Math. Monthly, 61, pp.623~626 (1954)
- K. Mehrez, "Generalized Huygens types inequalities for Bessel and modified Bessel functions of the first kind", arXiv:1601.01007v1, ~
- K. Mehrez, "Extension of Huygens type inequalities for Bessel and modified Bessel Functions of the first kinds", arXiv:1512.05798v1, ~
- M.E.H. Ismail, "On the variation with respect to a parameter of zeros of Bessel and q - Bessel functions", J. Math. Anal. Appl, 135(1), pp.187~207 (1988)
- E. Neuman, "On some inequalities involving trigonometric and hyperbolic functions with emphasis on the Cusa-Huygens, Wilker, and Huygens inequalities", Math. Inequal. Appl, 13(4), pp.715~723 (2010)
- S. Ponnusamy, "Asymptotic expansions and inequalities for hypergeometric functions", Mathematika, 44, pp.278~301 (1997)
- S. M. Sitnik, "Inequalities for Bessel functions", Dokl. Akad. Nauk SSSR, 340(1), pp.29~32 (1995)
- G. N. Watson, "A treatise on the theory of Bessel functions" (1944), Cambridge University Press