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Special formal series solutions of linear operator equations
TLDR
We characterize generalized hypergeometric series that solve a linear differential equation with polynomial coefficients at an ordinary point of the equation, and show that these solutions remain hypergeometry at any other ordinary point. Expand
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Conditions favorable to the existence of an undulating jump
Conclusions1.In analyzing the boundaries of development of an undulating jump, it is necessary to distinguish the conditions of existence of departing and approaching undulating jumps.2.The breakingExpand
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Resolving sequences of operators for linear ordinary differential and difference systems of arbitrary order
We introduce the notion of a resolving sequence of (scalar) operators for a given differential or difference system with coefficients in some differential or difference field K. We propose anExpand
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Procedures for searching local solutions of linear differential systems with infinite power series in the role of coefficients
TLDR
Construction of Laurent, regular, and formal (exponential–logarithmic) solutions of full-rank linear ordinary differential systems with the coefficients given by infinite, rather than truncated, series. Expand
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On exponential-logarithmic solutions of linear differential systems with power series coefficients
  • A. Ryabenko
  • Mathematics, Computer Science
  • Programming and Computer Software
  • 1 March 2015
TLDR
We propose an algorithm and its implementation in Maple that make it possible to construct a basis of the space of solutions of the full-rank system if the dimension of this space is known. Expand
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Laurent, Rational, and Hypergeometric Solutions of Linear q-Difference Systems of Arbitrary Order with Polynomial Coefficients
TLDR
In this paper, we consider direct algorithms for searching solutions to systems of linear q-difference equations with polynomial coefficients in the form of Laurent series. Expand
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A definite summation of hypergeometric terms of special kind
  • A. Ryabenko
  • Mathematics, Computer Science
  • Programming and Computer Software
  • 1 July 2011
TLDR
It is proposed to use simple preliminary examination of the term before applying the Zeilberger algorithm for hypergeometric summation. Expand
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Hypergeometric Solutions of First-Order Linear Difference Systems with Rational-Function Coefficients
TLDR
We propose an algorithm for finding hypergeometric solutions of scalar linear difference equations with rational-function coefficients with first-order systems of such equations. Expand
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Indicial rational functions of linear ordinary differential equations with polynomial coefficients
The notion of indicial rational function is introduced for ordinary differential equations with polynomial coefficients and polynomial right-hand sides, and algorithms for its construction areExpand
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