scholarly journals Closed Forms for Derangement Numbers in Terms of the Hessenberg Determinants

2016 ◽  
Author(s):  
Feng Qi ◽  
Jiao-Lian Zhao ◽  
Bai-Ni Guo
Keyword(s):  
Recurrence Relation ◽  
Generating Function ◽  
Higher Order ◽  
Order Derivative ◽  
Exponential Generating Function ◽  
Higher Order Derivative

In the paper, the authors find closed forms for derangement numbers in terms of the Hessenberg determinants, discover a recurrence relation of derangement numbers, present a formula for any higher order derivative of the exponential generating function of derangement numbers, and compute some related Hessenberg and tridiagonal determinants.

scholarly journals PID Control With Higher Order Derivative Degrees for IPDT Plant Models

IEEE Access ◽  
2021 ◽  
Vol 9 ◽  
pp. 2478-2495
Author(s):  
Mikulas Huba ◽  
Damir Vrancic ◽  
Pavol Bistak
Keyword(s):  
Pid Control ◽  
Higher Order ◽  
Order Derivative ◽  
Higher Order Derivative
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