• 제목/요약/키워드: modified Lommel functions

검색결과 2건 처리시간 0.015초

BOUNDS AND INEQUALITIES OF THE MODIFIED LOMMEL FUNCTIONS

  • Mondal, Saiful R.
    • 대한수학회논문집
    • /
    • 제34권2호
    • /
    • pp.573-583
    • /
    • 2019
  • 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, $Tur{\acute{a}}n$ type and reverse $Tur{\acute{a}}n$ type inequalities are given. A Rayleigh type function for the Lommel functions are derived and as an application, we obtain the Redheffer-type inequality.

CERTAIN GEOMETRIC PROPERTIES OF MODIFIED LOMMEL FUNCTIONS

  • Din, Muhey U;Yalcin, Sibel
    • 호남수학학술지
    • /
    • 제42권4호
    • /
    • pp.719-731
    • /
    • 2020
  • In this article, we find some sufficient conditions under which the modified Lommel function is close-to-convex with respect to - log(1 - z) and ${\frac{1}{2}}\;{\log}\;\({\frac{1+z}{1-z}}\)$. Starlikeness, convexity and uniformly close-to-convexity of the modified Lommel function are also discussed. Some results related to the H. Silverman are also the part of our investigation.