Telescoping Algorithms for $\Sigma^*$-Extensions via Complete Reductions | Paper Citation Record

Observation f1b43d41-57f9-4c9d-a608-75b91687a1a4 · outbound

This paper cites Harmonic Sums and Polylogarithms Generated by Cyclotomic Polynomials.

Telescoping Algorithms for $\Sigma^*$-Extensions via Complete Reductions Harmonic Sums and Polylogarithms Generated by Cyclotomic Polynomials

Reference 1

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Telescoping Algorithms for $\Sigma^*$-Extensions via Complete Reductions Unresolved cited work

Reference 2

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Telescoping Algorithms for $\Sigma^*$-Extensions via Complete Reductions Unresolved cited work

Reference 3

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This paper cites Abramov, Manuel Bronstein, Marko Petkov ˇsek, and Carsten Schneider.

Telescoping Algorithms for $\Sigma^*$-Extensions via Complete Reductions Abramov, Manuel Bronstein, Marko Petkov ˇsek, and Carsten Schneider

Reference 4

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Observation 19f950d0-750e-4891-a79e-72b031b10ce5 · outbound

This paper cites Bl¨ umlein and S.

Telescoping Algorithms for $\Sigma^*$-Extensions via Complete Reductions Bl¨ umlein and S

Reference 5

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Observation 25fc4215-a6da-4155-a47d-108b799bbdaf · outbound

This paper cites The three-loop polarized singlet anomalous dimensions from off-shell operator matrix elements.

Telescoping Algorithms for $\Sigma^*$-Extensions via Complete Reductions The three-loop polarized singlet anomalous dimensions from off-shell operator matrix elements

Reference 6

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Observation a407d684-1ade-494c-ba95-bad0c935bbca · outbound

This paper cites Hermite reduction and creative telescoping for hyperexponential functions.

Telescoping Algorithms for $\Sigma^*$-Extensions via Complete Reductions Hermite reduction and creative telescoping for hyperexponential functions

Reference 7

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Observation ce918962-643a-471e-9f4f-23b36aaaa18f · outbound

This paper cites Generalized hermite reduction, creative telescoping and definite integration of D-finite functions.

Telescoping Algorithms for $\Sigma^*$-Extensions via Complete Reductions Generalized hermite reduction, creative telescoping and definite integration of D-finite functions

Reference 8

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Observation df26c1ad-ac9d-4bae-9b9a-fab7e2f109e2 · outbound

This paper cites Additive normal forms and integration of differential fractions.J.

Telescoping Algorithms for $\Sigma^*$-Extensions via Complete Reductions Additive normal forms and integration of differential fractions.J

Reference 9

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Observation 0806a621-a214-4157-bc8b-2b7290a0e173 · outbound

This paper cites A p-adic study of the partial sums of the harmonic series.Experimental Mathematics, 3(4):287–302, 1994.

Telescoping Algorithms for $\Sigma^*$-Extensions via Complete Reductions A p-adic study of the partial sums of the harmonic series.Experimental Mathematics, 3(4):287–302, 1994

Reference 10

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Observation 5c1a077c-58b5-4655-ad9e-92f55c97e74f · outbound

This paper cites On solutions of linear ordinary difference equations in their coefficient field.

Telescoping Algorithms for $\Sigma^*$-Extensions via Complete Reductions On solutions of linear ordinary difference equations in their coefficient field

Reference 11

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Observation bbc36134-d6a9-48ab-998b-1a45e23ab36c · outbound

This paper cites A Unified Reduction for Hypergeometric and q-Hypergeometric Creative Telescoping.

Telescoping Algorithms for $\Sigma^*$-Extensions via Complete Reductions A Unified Reduction for Hypergeometric and q-Hypergeometric Creative Telescoping

Reference 12

Resolution: verified exact; local_arxiv, observed 2026-08-07T05:13:20.963908Z

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Observation a0ee30f2-80f9-4028-b6b1-eab92e6f1a14 · outbound

This paper cites Lazy Hermite reduction and creative telescoping for algebraic functions.

Telescoping Algorithms for $\Sigma^*$-Extensions via Complete Reductions Lazy Hermite reduction and creative telescoping for algebraic functions

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T05:13:21.882753Z

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Observation 45b0aaa0-68da-4509-af86-a82ba314ffde · outbound

This paper cites Hermite reduction for D-finite functions via integral bases.

Telescoping Algorithms for $\Sigma^*$-Extensions via Complete Reductions Hermite reduction for D-finite functions via integral bases

Reference 14

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Observation 3596af2a-224c-499d-ba25-d0ddf8e9ec8e · outbound

This paper cites A modified Abramov-Petkov ˇsek reduction and creative telescoping for hypergeometric terms.

Telescoping Algorithms for $\Sigma^*$-Extensions via Complete Reductions A modified Abramov-Petkov ˇsek reduction and creative telescoping for hypergeometric terms

Reference 15

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Observation 8e9449e3-c253-4e89-bbbe-37e92d90c4e1 · outbound

This paper cites Reduction-based creative telescoping for algebraic functions.

Telescoping Algorithms for $\Sigma^*$-Extensions via Complete Reductions Reduction-based creative telescoping for algebraic functions

Reference 16

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Observation e0b7dff7-6a23-4525-8f73-7308f8b7e1ce · outbound

This paper cites Reduction-based creative telescoping for Fuchsian D-finite functions.J.

Telescoping Algorithms for $\Sigma^*$-Extensions via Complete Reductions Reduction-based creative telescoping for Fuchsian D-finite functions.J

Reference 17

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Observation 01d135c6-1961-4367-95af-2e3288b19beb · outbound

This paper cites Complete reduction for derivatives in a primitive tower, 2025.

Telescoping Algorithms for $\Sigma^*$-Extensions via Complete Reductions Complete reduction for derivatives in a primitive tower, 2025

Reference 18

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Observation 2b47caef-ffd4-48ac-982c-43a1570323ca · outbound

This paper cites A𝑞-analogue of the modified Abramov-Petkovˇsek reduction.

Telescoping Algorithms for $\Sigma^*$-Extensions via Complete Reductions A𝑞-analogue of the modified Abramov-Petkovˇsek reduction

Reference 19

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Observation 7926e4aa-6917-4e73-af32-d233970d097a · outbound

This paper cites PhD thesis, Chinese Academy of Sciences, Beijing, China, May 2024.

Telescoping Algorithms for $\Sigma^*$-Extensions via Complete Reductions PhD thesis, Chinese Academy of Sciences, Beijing, China, May 2024

Reference 20

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T05:13:21.389629Z

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Observation 6822dee7-34b6-4f32-a052-b5c215052b7e · outbound

This paper cites William Gosper, Jr.

Telescoping Algorithms for $\Sigma^*$-Extensions via Complete Reductions William Gosper, Jr

Reference 21

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T05:13:21.374536Z

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Observation ba68bf5d-365b-4e1d-a1e5-2dec7ba34974 · outbound

This paper cites Summation in finite terms.J.

Telescoping Algorithms for $\Sigma^*$-Extensions via Complete Reductions Summation in finite terms.J

Reference 22

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T05:13:21.361298Z

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Observation 2585b9ad-150a-4e51-8328-046860ccff62 · outbound

This paper cites Theory of summation in finite terms.J.

Telescoping Algorithms for $\Sigma^*$-Extensions via Complete Reductions Theory of summation in finite terms.J

Reference 23

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Observation 6009b922-b34a-4e11-9036-f3a2673fe4b1 · outbound

This paper cites Springer Cham, Switzerland, 2023.

Telescoping Algorithms for $\Sigma^*$-Extensions via Complete Reductions Springer Cham, Switzerland, 2023

Reference 24

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T05:13:21.331516Z

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Observation b0e72790-894f-4e15-b8a3-979d1e4acfa5 · outbound

This paper cites Indefinite summation with unspecified summands.Discrete Math., 306(17):2073–2083, 2006.

Telescoping Algorithms for $\Sigma^*$-Extensions via Complete Reductions Indefinite summation with unspecified summands.Discrete Math., 306(17):2073–2083, 2006

Reference 25

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Observation a62bcfdf-5da0-4862-bfd3-ba5433f31571 · outbound

This paper cites Knuth.The Art of Computer Programming, volume 1: Fundamental Algorithms.

Telescoping Algorithms for $\Sigma^*$-Extensions via Complete Reductions Knuth.The Art of Computer Programming, volume 1: Fundamental Algorithms

Reference 26

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T05:13:21.302014Z

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Observation 283bf7a3-115e-45ae-98c2-c64e69a214ab · outbound

This paper cites Koornwinder.

Telescoping Algorithms for $\Sigma^*$-Extensions via Complete Reductions Koornwinder

Reference 27

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T05:13:21.287092Z

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Observation 87b93fc5-17ec-4e46-b2e3-af2deb159cc1 · outbound

This paper cites Greatest factorial factorization and symbolic summation.J.

Telescoping Algorithms for $\Sigma^*$-Extensions via Complete Reductions Greatest factorial factorization and symbolic summation.J

Reference 28

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Observation bf7b96de-1834-473c-8772-368e5135e1f4 · outbound

This paper cites A Mathematica𝑞-analogue of Zeilberger’s algorithm based on an algebraically motivated approach to𝑞-hypergeometric telescoping.

Telescoping Algorithms for $\Sigma^*$-Extensions via Complete Reductions A Mathematica𝑞-analogue of Zeilberger’s algorithm based on an algebraically motivated approach to𝑞-hypergeometric telescoping

Reference 29

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T05:13:21.257716Z

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Observation 0e50f56f-f574-4bc1-9727-4da9352e1240 · outbound

This paper cites Computer proofs of a new family of harmonic number identities.

Telescoping Algorithms for $\Sigma^*$-Extensions via Complete Reductions Computer proofs of a new family of harmonic number identities

Reference 30

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T05:13:21.243557Z

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Observation 06994ab3-ec03-4b94-a10c-41e6ea09dd36 · outbound

This paper cites A Mathematica version of Zeilberger’s algorithm for proving bi- nomial coefficient identities.J.

Telescoping Algorithms for $\Sigma^*$-Extensions via Complete Reductions A Mathematica version of Zeilberger’s algorithm for proving bi- nomial coefficient identities.J

Reference 31

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T05:13:21.229578Z

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Observation ae548970-8941-499e-b635-700ef2a7fe7c · outbound

This paper cites Wilf, and Doron Zeilberger.𝐴=𝐵.

Telescoping Algorithms for $\Sigma^*$-Extensions via Complete Reductions Wilf, and Doron Zeilberger.𝐴=𝐵

Reference 32

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T05:13:21.215411Z

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Observation 7579b646-700e-49e9-a9b8-7e9aad6c5b79 · outbound

This paper cites PhD thesis, RISC-Linz, Johannes Kepler University, May 2001.

Telescoping Algorithms for $\Sigma^*$-Extensions via Complete Reductions PhD thesis, RISC-Linz, Johannes Kepler University, May 2001

Reference 33

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T05:13:21.200365Z

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Observation 477d89ed-4b67-44f7-8860-04cdc80ac363 · outbound

This paper cites Symbolic summation with single-nested sum extensions.

Telescoping Algorithms for $\Sigma^*$-Extensions via Complete Reductions Symbolic summation with single-nested sum extensions

Reference 34

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T05:13:21.186465Z

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Observation d0a45b65-d9bd-4065-aa10-66ea2c12bed3 · outbound

This paper cites Finding telescopers with minimal depth for indefinite nested sum and product expressions.

Telescoping Algorithms for $\Sigma^*$-Extensions via Complete Reductions Finding telescopers with minimal depth for indefinite nested sum and product expressions

Reference 35

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Observation 329289f6-827c-4bba-964d-5a7680ec2975 · outbound

This paper cites Product representations inΠΣ-fields.Ann.

Telescoping Algorithms for $\Sigma^*$-Extensions via Complete Reductions Product representations inΠΣ-fields.Ann

Reference 36

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T05:13:21.158807Z

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Observation 0df2f1c8-489d-452a-ab60-2911febffba0 · outbound

This paper cites Symbolic summation assists combinatorics.S ´em.

Telescoping Algorithms for $\Sigma^*$-Extensions via Complete Reductions Symbolic summation assists combinatorics.S ´em

Reference 37

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T05:13:21.144536Z

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Observation 8ede3b0e-db57-46ec-94fe-c757f3fee1a3 · outbound

This paper cites Simplifying sums inΠΣ ∗-extensions.J.

Telescoping Algorithms for $\Sigma^*$-Extensions via Complete Reductions Simplifying sums inΠΣ ∗-extensions.J

Reference 38

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Observation 47aff897-8d0a-409a-8336-998a7b2f5b31 · outbound

This paper cites A refined difference field theory for symbolic summation.J.

Telescoping Algorithms for $\Sigma^*$-Extensions via Complete Reductions A refined difference field theory for symbolic summation.J

Reference 39

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T05:13:21.115597Z

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Observation ca6e766d-99e9-4b28-a71c-8a6274d221e4 · outbound

This paper cites Parameterized Telescoping Proves Algebraic Independence of Sums.

Telescoping Algorithms for $\Sigma^*$-Extensions via Complete Reductions Parameterized Telescoping Proves Algebraic Independence of Sums

Reference 40

Resolution: verified exact; local_arxiv, observed 2026-08-07T05:13:20.943532Z

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Observation edae1fd2-8f5c-49bc-8391-7c95a2b1048a · outbound

This paper cites Structural theorems for symbolic summation.Appl.

Telescoping Algorithms for $\Sigma^*$-Extensions via Complete Reductions Structural theorems for symbolic summation.Appl

Reference 41

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T05:13:21.101740Z

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Observation da2a1241-740b-42e2-a81c-a5fde466385b · outbound

This paper cites Fast Algorithms for Refined Parameterized Telescoping in Difference Fields.

Telescoping Algorithms for $\Sigma^*$-Extensions via Complete Reductions Fast Algorithms for Refined Parameterized Telescoping in Difference Fields

Reference 42

Resolution: verified exact; local_arxiv, observed 2026-08-07T05:13:20.923139Z

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Observation dcba3d0e-940f-4018-9669-bcb167a41df7 · outbound

This paper cites A difference ring theory for symbolic summation.J.

Telescoping Algorithms for $\Sigma^*$-Extensions via Complete Reductions A difference ring theory for symbolic summation.J

Reference 43

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T05:13:21.086814Z

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Observation a873f4ae-7354-4717-a74f-351b1451e331 · outbound

This paper cites Summation theory II: Characterizations of𝑅ΠΣ ∗-extensions and algorithmic aspects.J.

Telescoping Algorithms for $\Sigma^*$-Extensions via Complete Reductions Summation theory II: Characterizations of𝑅ΠΣ ∗-extensions and algorithmic aspects.J

Reference 44

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T05:13:21.070354Z

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Observation e1e94771-0161-47df-a86b-7149d4925c06 · outbound

This paper cites Term algebras, canonical representations and difference ring theory for sym- bolic summation.

Telescoping Algorithms for $\Sigma^*$-Extensions via Complete Reductions Term algebras, canonical representations and difference ring theory for sym- bolic summation

Reference 45

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T05:13:21.055721Z

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Observation bfdfd17f-5471-4bfd-944a-06cd5cbcbe10 · outbound

This paper cites The Absent-Minded Passengers Problem: A Motivating Challenge Solved by Computer Algebra.

Telescoping Algorithms for $\Sigma^*$-Extensions via Complete Reductions The Absent-Minded Passengers Problem: A Motivating Challenge Solved by Computer Algebra

Reference 46

Resolution: verified exact; local_arxiv, observed 2026-08-07T05:13:20.903406Z

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Observation 5a8b5f6e-c9ca-4ac6-83f8-fd7916d995b2 · outbound

This paper cites Refined telescoping algorithms in $R\Pi\Sigma$-extensions to reduce the degrees of the denominators.

Telescoping Algorithms for $\Sigma^*$-Extensions via Complete Reductions Refined telescoping algorithms in $R\Pi\Sigma$-extensions to reduce the degrees of the denominators

Reference 47

Resolution: verified exact; local_arxiv, observed 2026-08-07T05:13:20.881915Z

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Observation 544fae7b-6506-416a-a7dd-e55047a9307c · outbound

This paper cites Constructing reductions for creative telescoping: the general differentially finite case.Appl.

Telescoping Algorithms for $\Sigma^*$-Extensions via Complete Reductions Constructing reductions for creative telescoping: the general differentially finite case.Appl

Reference 48

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T05:13:21.041542Z

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Observation 28fe5880-3c64-4066-b562-69975430f89c · outbound

This paper cites A holonomic systems approach to special functions identities.J.

Telescoping Algorithms for $\Sigma^*$-Extensions via Complete Reductions A holonomic systems approach to special functions identities.J

Reference 49

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T05:13:21.026792Z

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Observation 7a24d7c0-ad83-44d8-9247-6d066dbb3773 · outbound

This paper cites The method of creative telescoping.J.

Telescoping Algorithms for $\Sigma^*$-Extensions via Complete Reductions The method of creative telescoping.J

Reference 50

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T05:13:21.009915Z

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