In mathematics, a Liouvillian function is an elementary function or (recursively) the integral of a Liouvillian function. More explicitly, it is a… (More)

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2018

2018

- Sergei A. Abramov, Marko Petkovsek, Helena Zakrajsek
- ArXiv
- 2018

While Liouvillian sequences are closed under many operations, simple examples show that they are not closed under convolution… (More)

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2016

2016

- Oscar Martinez-Fuentes, Rafael Martínez-Guerra
- 2016 American Control Conference (ACC)
- 2016

In this paper the problem of generalized synchronization, is studied for chaotic Liouvillian nonlinear fractional systems of… (More)

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2012

2012

- Alberto Llorente, Jorge Mozo-Fernández
- ACM Comm. Computer Algebra
- 2012

Theorem 1 There exists a function I : N → N such that, if (1) has a non-zero Liouvillian solution, then there exist an algebraic… (More)

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2011

2011

- Clemens G. Raab
- ACM Comm. Computer Algebra
- 2011

Definition: We call a differential field (F,D) = (C(t1, . . . , tn), D) admissible, if 1. all ti are algebraically independent… (More)

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2007

2007

- Francis P. Temme
- 2007

Augmented quasiparticle (QP) mappings, as applied to indistinguishable point sets of (Liouvillian) democratic-recoupled (DR… (More)

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2002

2002

- Manuel Bronstein, Sébastien Lafaille
- ISSAC
- 2002

We describe a new algorithm for computing special function solutions of the form <i>y</i>(<i>x</i>) = <i>m</i>(<i>x</i>)<i>F</i… (More)

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2001

2001

We present an algorithm to solve First Order Ordinary Differential Equations (FOODEs) extending the Prelle-Singer (PS) Method… (More)

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1995

1995

- Felix Ulmer, Jacques-Arthur Weil
- J. Symb. Comput.
- 1995

Let L(y ) = y" + a l y ~ + aoy be a second order equation with coefficients in a differential field k whose field of constants C… (More)

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Highly Cited

1988

Highly Cited

1988

- Michael F. Singer
- ISSAC
- 1988

Liouvillian functions are functions that are built up from rational functions using exponentiation, integration, and algebraic… (More)

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1986

1986

- Paul H. Knowles
- SYMSAC
- 1986

In this paper, we discuss a decision procedure for the indefinite integration of transcendental Liouvillian functions in terms of… (More)

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