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Order Bounds for Hypergeometric and q-Hypergeometric Creative Telescoping
Hui Huang
Leveraging a general framework adapted from symbolic integration, a unified reduction-based algorithm for computing telescopers of minimal order for hypergeometric and q-hypergeome…
Complete Reduction for Derivatives in a Transcendental Liouvillian Extension
Shaoshi Chen, Hao Du, Yiman Gao +3
Transcendental Liouvillian extensions are differential fields, in which one can model poly-logarithmic, hyperexponential, and trigonometric functions, logarithmic integrals, and th…
Telescoping Algorithms for -Extensions via Complete Reductions
Shaoshi Chen, Yiman Gao, Hui Huang +1
A complete reduction on a difference field is a linear operator that enables one to decompose an element of the field as the sum of a summable part and a remainder such that the gi…
A Unified Reduction for Hypergeometric and q-Hypergeometric Creative Telescoping
Shaoshi Chen, Hao Du, Yiman Gao +2
We adapt the theory of normal and special polynomials from symbolic integration to the summation setting, and then built up a general framework embracing both the usual shift case…