Divided Differences Calculus in Matrix Representation

  • Robert M. YamaleevEmail author
Original Paper


A systematic description of actions of the divided differences operators on power and exponential functions is given. The results of actions of these operators on entire functions are presented by the matrices whose elements are functions of coefficients of a characteristic (pivot) polynomial. Effective algorithms of calculation of the matrices are constructed using the properties of the companion matrix of the pivoting polynomial. Degeneration of the roots of the pivot polynomial reduces the n-order divided differences operator to \(n-1\) order operator of differentiation. The exponential type invariant functions with respect to higher order derivatives are constructed.


Vandermonde matrix Divided differences Trigonometry Pascal matrix Polynomial Invariant functions 



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Copyright information

© Springer Nature India Private Limited 2019

Authors and Affiliations

  1. 1.Joint Institute for Nuclear ResearchLITDubnaRussia

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