Extension of Algorithms for D-finite functions [DK15]

Project Lead

Project Duration

01/10/2014 - 31/12/2020

Project URL

Go to Website

Publications

2019

[Jimenez Pastor]

A Computable Extension for Holonomic Functions: DD-Finite Functions

Jiménez-Pastor Antonio, Pillwein Veronika

Journal of Symbolic Computation 94, pp. 90-104. September-October 2019. ISSN 0747-7171. [url]
[bib]
@article{RISC5831,
author = {Jiménez-Pastor Antonio and Pillwein Veronika},
title = {{A Computable Extension for Holonomic Functions: DD-Finite Functions}},
language = {english},
abstract = {Differentiably finite (D-finite) formal power series form a large class of useful functions for which a variety of symbolic algorithms exists. Among these methods are several closure properties that can be carried out automatically. We introduce a natural extension of these functions to a larger class of computable objects for which we prove closure properties. These are again algorithmic. This extension can be iterated constructively preserving the closure properties},
journal = {Journal of Symbolic Computation},
volume = {94},
pages = {90--104},
isbn_issn = {ISSN 0747-7171},
year = {2019},
month = {September-October},
refereed = {yes},
length = {15},
url = {https://doi.org/10.1016/j.jsc.2018.07.002}
}

2018

[Jimenez Pastor]

Algorithmic Arithmetics with DD-Finite Functions

Jiménez-Pastor Antonio, Pillwein Veronika

In: Proceedings of the 2018 ACM on International Symposium on Symbolic and Algebraic Computation, Arreche Carlos (ed.), ISSAC '18 , pp. 231-237. 2018. ACM, New York, NY, USA, ISBN 978-1-4503-5550-6. [url]
[bib]
@inproceedings{RISC5730,
author = {Jiménez-Pastor Antonio and Pillwein Veronika},
title = {{Algorithmic Arithmetics with DD-Finite Functions}},
booktitle = {{Proceedings of the 2018 ACM on International Symposium on Symbolic and Algebraic Computation}},
language = {english},
series = {ISSAC '18},
pages = {231--237},
publisher = {ACM},
address = {New York, NY, USA},
isbn_issn = {ISBN 978-1-4503-5550-6},
year = {2018},
editor = {Arreche Carlos},
refereed = {yes},
keywords = {algorithms, closure properties, holonomic functions},
length = {7},
url = {http://doi.acm.org/10.1145/3208976.3209009}
}
[Pillwein]

Positivity of the Gillis-Reznick-Zeilberger rational function

V. Pillwein

Technical report no. 18-05 in RISC Report Series, Research Institute for Symbolic Computation (RISC), Johannes Kepler University Linz, Schloss Hagenberg, 4232 Hagenberg, Austria. 2018. [pdf]
[bib]
@techreport{RISC5612,
author = {V. Pillwein},
title = {{Positivity of the Gillis-Reznick-Zeilberger rational function}},
language = {english},
number = {18-05},
year = {2018},
length = {12},
type = {RISC Report Series},
institution = {Research Institute for Symbolic Computation (RISC), Johannes Kepler University Linz},
address = {Schloss Hagenberg, 4232 Hagenberg, Austria}
}
[Pillwein]

Difference equation satisfied by the Stieltjes transform of a sequence

D. Dominici, V. Pillwein

Doctoral Program "Computational Mathematics". Technical report no. DK Report 2018-11, 2018. [url] [pdf]
[bib]
@techreport{RISC5827,
author = {D. Dominici and V. Pillwein},
title = {{Difference equation satisfied by the Stieltjes transform of a sequence}},
language = {english},
number = {DK Report 2018-11},
year = {2018},
institution = {Doctoral Program "Computational Mathematics"},
length = {13},
url = {https://www.dk-compmath.jku.at/publications/dk-reports/2018-12-12/}
}

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