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Hypergeometric Solutions of Linear Recurrences with Polynomial Coefficents
  • M. Petkovsek
  • Computer Science, Mathematics
  • J. Symb. Comput.
  • 1 August 1992
TLDR
We describe algorithm Hyper which can be used to find all hypergeometric solutions of linear recurrences with polynomial coefficients. Expand
  • 256
  • 18
  • PDF
An Introduction to Pseudo-Linear Algebra
TLDR
Pseudo-linear algebra is the study of common properties of linear differential and difference operators. Expand
  • 196
  • 13
  • PDF
On polynomial solutions of linear operator equations
TLDR
The algorithm described here extends the algorithm to nd all polynomial solutions of di erential and di erence equations that was given in [1, 2] to more general operators. Expand
  • 116
  • 9
Rational Normal Forms and Minimal Decompositions of Hypergeometric Terms
TLDR
We describe a multiplicative normal form for rational functions which exhibits the shift structure of the factors, and investigate its properties. Expand
  • 48
  • 8
  • PDF
The effect of high frequency electric pulses on muscle contractions and antitumor efficiency in vivo for a potential use in clinical electrochemotherapy.
Muscle contractions present the main source of unpleasant sensations for patients undergoing electrochemotherapy. The contractions are a consequence of high voltage pulse delivery. Relatively lowExpand
  • 95
  • 7
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Minimal decomposition of indefinite hypergeometric sums
TLDR
We present an algorithm which, given a hypergeometric term <i>T</i>(<i>n</i>), constructs hypergeometry terms <i T</i><subscrpt>1</subscRpt>(< i>N</i>) such that the sum of the terms is minimal in some sense. Expand
  • 26
  • 7
  • PDF
Linear recurrences with constant coefficients: the multivariate case
TLDR
We show that the multivariate case is much richer: even though initial conditions have rational generating functions, the corresponding solutions can have generating functions which are algebraic but not rational, D-finite but not algebraic, and even non-Finite. Expand
  • 150
  • 5
  • PDF
Letter graphs and well-quasi-order by induced subgraphs
  • M. Petkovsek
  • Computer Science, Mathematics
  • Discret. Math.
  • 6 February 2002
TLDR
We show that the class of k-letter graphs is well-quasi-ordered by the induced subgraph relation, and that it has a finite set of minimal forbidden subgraphs. Expand
  • 41
  • 5
  • PDF
D'Alembertian solutions of linear differential and difference equations
TLDR
D'Alembertian solutions of differential (resp. difference) equations are those expressible as nested indefinite integrals of hyperexponential functions. Expand
  • 71
  • 4
Techniques of signal generation required for electropermeabilization. Survey of electropermeabilization devices.
Electropermeabilization is a phenomenon that transiently increases permeability of the cell plasma membrane. In the state of high permeability, the plasma membrane allows ions, small and largeExpand
  • 112
  • 3
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