A diagonal recurrence relation for the Stirling numbers of the first kind. (English) Zbl 1488.11060
Summary: 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.
Keywords:
diagonal recurrence relation; inhomogeneous linear ordinary dierential equation; Stirling numbers of the first kind; Lerch transcendent; complete monotonicitySoftware:
DLMFReferences:
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| [37] | Feng Qi (Received 05.04.2017) Institute of Mathematics (Revised 01.10.2017) |
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