21,664 research outputs found
Monotonicity and Logarithmic Convexity for a Class of Elementary Functions Involving the Exponential Function
Properties of modified Bessel functions and completely monotonic degrees of differences between exponential and trigamma functions
In the paper, the author establishes inequalities, monotonicity, convexity,
and unimodality for functions concerning the modified Bessel functions of the
first kind and compute the completely monotonic degrees of differences between
the exponential and trigamma functions.Comment: 21 page
A Completely Monotonic Function Involving Divided Difference of Psi Function and an Equivalent Inequality Involving Sum
In this paper, a function involving the divided difference of the
psi function is proved to be completely monotonic, a class of inequalities involving
sum are founded, and an equivalent relation between the complete
monotonicity and one of the class of inequalities is established
Jordan's Inequality: Refinements, Generalizations, Applications and Related Problems
This is an expository article. Some developments on refinements,
generalizations, applications of Jordanâs inequality and related problems, including
some estimates for three classes of complete elliptic integrals and several
proofs of Wilkerâs inequality, are summarized
Properties of three functions relating to the exponential function and the existence of partitions of unity
In the paper, the author studies properties of three functions relating to
the exponential function and the existence of partitions of unity, including
accurate and explicit computation of their derivatives, analyticity, complete
monotonicity, logarithmically complete monotonicity, absolute monotonicity, and
the like.Comment: 5 page
Diagonal recurrence relations for the Stirling numbers of the first kind
In the paper, the author presents diagonal recurrence relations for the
Stirling numbers of the first kind. As by-products, the author also recovers
three explicit formulas for special values of the Bell polynomials of the
second kind.Comment: 7 page
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