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This article studies the monotonicity, log-convexity of the modified Lommel functions by using its power series and infinite product representation. Some properties for the ratio of the modified Lommel functions with the Lommel function, $\sinh$ and $\cosh$ are also discussed. As a consequence, Tur\'an type and reverse Tur\'an type inequalities are given. A Rayleigh type function for the Lommel functions are derived and as an application, we obtain the Redheffer-type inequality.
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참고문헌 (19)
참고문헌 신청
G. D. Anderson / 1993 / Inequalities for quasiconformal mappings in space / Pacic J. Math 160(1):1~18
A. W. Babister / 1967 / Transcendental Functions Satisfying Nonhomogeneous Linear Dierential Equations / The Macmillan Co
Baricz / 2016 / Turan-type inequalities for some Lommel functions of the rst kind / Proc. Edinb. Math. Soc 59(3):569~579
M. Biernacki / 1955 / On the monotonity of certain functionals in the theory of analytic functions / Ann. Univ. Mariae Curie-Sk lodowska. Sect. A 9:135~147
Y.-M. Chiang / 2011 / special functions and related polynomials / J. Reine Angew. Math 651:127~164
A. W. Babister / 1967 / Transcendental Functions Satisfying Nonhomogeneous Linear Dierential Equations / The Macmillan Co
Baricz / 2016 / Turan-type inequalities for some Lommel functions of the rst kind / Proc. Edinb. Math. Soc 59(3):569~579
M. Biernacki / 1955 / On the monotonity of certain functionals in the theory of analytic functions / Ann. Univ. Mariae Curie-Sk lodowska. Sect. A 9:135~147
Y.-M. Chiang / 2011 / special functions and related polynomials / J. Reine Angew. Math 651:127~164
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