Bai-Ni Guo

Complete monotonicity of some functions involving polygamma functions

In the present paper, we establish necessary and sufficient conditions for the functions x^@a|@j^(^i^)(x+@b)| and @a|@j^(^i^)(x+@b)|-x|@j^(^i^+^1^)(x+@b)| respectively to be monotonic and completely monotonic on (0,~), where i@?N, @a>0 and @b>=0 are scalars, and @j^(^i^)(x) are polygamma functions.

Refinements, Generalizations, and Applications of Jordan's Inequality and Related Problems

This is a survey and expository article. Some new developments on refinements, generalizations, and applications of Jordans inequality and related problems, including some results about Wilker-Anglesios inequality, some estimates for three kinds of complete elliptic integrals, and several inequalities for the remainder of power series expansion of the exponential function, are summarized.

Some identities and an explicit formula for Bernoulli and Stirling numbers

In the paper, the author establishes some identities which show that the functions

Sharp inequalities for the psi function and harmonic numbers

\frac1{(1-e^{\pm t})^k}

TWO NEW PROOFS OF THE COMPLETE MONOTONICITY OF A FUNCTION INVOLVING THE PSI FUNCTION

and the derivatives

GENERALIZATIONS OF BERNOULLI NUMBERS AND POLYNOMIALS

\bigl(\frac1{e^{\pm t}-1}\bigr)^{(i)}

WENDEL'S AND GAUTSCHI'S INEQUALITIES: REFINEMENTS, EXTENSIONS, AND A CLASS OF LOGARITHMICALLY COMPLETELY MONOTONIC FUNCTIONS

can be expressed each other by linear combinations with coefficients involving the combinatorial numbers and the Stirling numbers of the second kind, where

Complete monotonicity of a function involving the divided difference of digamma functions

t\ne0

A CLASS OF COMPLETELY MONOTONIC FUNCTIONS INVOLVING DIVIDED DIFFERENCES OF THE PSI AND TRI-GAMMA FUNCTIONS AND SOME APPLICATIONS

and

A completely monotonic function involving the tri-gamma function and with degree one☆

i,k\in\mathbb{N}