Creative Telescoping for Holonomic Functions

Abstract

The aim of this article is twofold: on the one hand it is intended to serve as a gentle introduction to the topic of creative telescoping, from a practical point of view; for this purpose its application to several problems is exemplified. On the other hand, this chapter has the flavour of a survey article: the developments in this area during the last two decades are sketched and a selection of references is compiled in order to highlight the impact of creative telescoping in numerous contexts.

Tutorial and survey article, 24 pages

References in corpus (4)

• A Fast Approach to Creative Telescoping
• Modern Summation Methods and the Computation of 2- and 3-loop Feynman Diagrams
• Differential Equations for Algebraic Functions
• Ising n-fold integrals as diagonals of rational functions and integrality of series expansions: integrality versus modularity

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• The SAGEX Review on Scattering Amplitudes, Chapter 4: Multi-loop Feynman Integrals
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• Lattice Green Functions: the d-dimensional face-centred cubic lattice, d=8, 9, 10, 11, 12
• Efficient Algorithms for Mixed Creative Telescoping
• Binomial Determinants for Tiling Problems Yield to the Holonomic Ansatz
• A case study for $\zeta (4)$
• Master Lovas-Andai and Equivalent Formulas Verifying the $\frac{8}{33}$ Two-Qubit Hilbert-Schmidt Separability Probability and Companion Rational-Valued Conjectures
• Parallel Telescoping and Parameterized Picard--Vessiot Theory
• Good pivots for small sparse matrices
• Lazy Hermite Reduction and Creative Telescoping for Algebraic Functions
• Exceptional Lattice Green's Functions
• On the length of integers in telescopers for proper hypergeometric terms