A holonomic systems approach to special functions identities
Journal of Computational and Applied Mathematics
Automatic average-case analysis of algorithms
Theoretical Computer Science - Theme issue on the algebraic and computing treatment of noncommutative power series
GFUN: a Maple package for the manipulation of generating and holonomic functions in one variable
ACM Transactions on Mathematical Software (TOMS)
Effective asymptotics of linear recurrences with rational coefficients
FPSAC '93 Proceedings of the 5th conference on Formal power series and algebraic combinatorics
Asymptotic enumeration methods
Handbook of combinatorics (vol. 2)
Asymptotic behavior of a Poincaré recurrence system
Journal of Approximation Theory
Fast evaluation of holonomic functions
Theoretical Computer Science - Special issue on real numbers and computers
Fast evaluation of holonomic functions near and in regular singularities
Journal of Symbolic Computation
Improved validated bounds for Taylor coefficients and for Taylor remainder series
Journal of Computational and Applied Mathematics - Proceedings of the international conference on recent advances in computational mathematics
ACM Transactions on Mathematical Software (TOMS)
On Taylor Model Based Integration of ODEs
SIAM Journal on Numerical Analysis
Analytic Combinatorics
NumGfun: a package for numerical and analytic computation with D-finite functions
Proceedings of the 2010 International Symposium on Symbolic and Algebraic Computation
The dynamic dictionary of mathematical functions (DDMF)
ICMS'10 Proceedings of the Third international congress conference on Mathematical software
Stokes phenomenon: graphical visualization and certified computation
Proceedings of the 2011 International Workshop on Symbolic-Numeric Computation
A note on the space complexity of fast D-finite function evaluation
CASC'12 Proceedings of the 14th international conference on Computer Algebra in Scientific Computing
Termination conditions for positivity proving procedures
Proceedings of the 38th international symposium on International symposium on symbolic and algebraic computation
Univariate polynomial solutions of algebraic difference equations
Journal of Symbolic Computation
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We describe an algorithm that takes as input a complex sequence (u"n) given by a linear recurrence relation with polynomial coefficients along with initial values, and outputs a simple explicit upper bound (v"n) such that |u"n|@?v"n for all n. Generically, the bound is tight, in the sense that its asymptotic behaviour matches that of u"n. We discuss applications to the evaluation of power series with guaranteed precision.