Preprint Article Version 1 NOT YET PEER-REVIEWED

Some Properties of a Solution to a Family of Inhomogeneous Linear Ordinary Differential Equations

Feng Qi 1,2,3,* and Bai-Ni Guo 4
  1. Institute of Mathematics, Henan Polytechnic University, Jiaozuo City, Henan Province 454010, China
  2. College of Mathematics, Inner Mongolia University for Nationalities, Tongliao City, Inner Mongolia Autonomous Region 028043, China
  3. Department of Mathematics, College of Science, Tianjin Polytechnic University, Tianjin City 300387, China
  4. School of Mathematics and Informatics, Henan Polytechnic University, Jiaozuo City, Henan Province 454010, China
Version 1 : Received: 29 November 2016 / Approved: 29 November 2016 / Online: 29 November 2016 (08:00:53 CET)

How to cite: Qi, F.; Guo, B. Some Properties of a Solution to a Family of Inhomogeneous Linear Ordinary Differential Equations. Preprints 2016, 2016110146 (doi: 10.20944/preprints201611.0146.v1). Qi, F.; Guo, B. Some Properties of a Solution to a Family of Inhomogeneous Linear Ordinary Differential Equations. Preprints 2016, 2016110146 (doi: 10.20944/preprints201611.0146.v1).

Abstract

In the paper, the authors present an explicit form for a family of inhomogeneous linear ordinary differential equations, find a more significant expression for all derivatives of a function related to the solution to the family of inhomogeneous linear ordinary differential equations in terms of the Lerch transcendent, establish an explicit formula for computing all derivatives of the solution to the family of inhomogeneous linear ordinary differential equations, acquire the absolute monotonicity, complete monotonicity, the Bernstein function property of several functions related to the solution to the family of inhomogeneous linear ordinary differential equations, discover a diagonal recurrence relation of the Stirling numbers of the first kind, and derive an inequality for bounding the logarithmic function.

Subject Areas

explicit form; inhomogeneous linear ordinary differential equation; derivative; Lerch transcendent; absolute monotonicity; complete monotonicity; Bernstein function; inequality; diagonal recurrence relation; Stirling numbers of the first kind; logarithmic function

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