Inversion Techniques and Combinatorial Identities

Chu, Wenchang

doi:10.1007/978-1-4613-3635-8_3

Cited by 34 publications

(30 citation statements)

References 14 publications

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“…Krattenthaler derived his generalization of Carlitz's matrix inversion in 1989, using methods he developed in [39]. Shortly thereafter, it was rediscovered in [19], using telescoping methods. An elementary proof may also be found in [51].…”

Section: The Factor [(And1)mentioning

confidence: 99%

“…In addition, if we set a j =ap j and b j =q j for all j, we obtain (1.6). Identity (1.9) may be extended to the summation theorem [19]: Theorem 1.10 (Chu). Let (a i ), (b i ) be arbitrary sequences, c be indeterminate, N be a nonnegative integer, and suppose that none of the denominators in (1.11) vanish.…”

Section: The Factor [(And1)mentioning

confidence: 99%

“…All the matrix inversions mentioned above, including those of Bressoud and Gasper, are special cases of Krattenthaler's matrix inversion. Further ahead in this section, we present an extension of Kratenthaler's matrix inversion to a general summation theorem, first found by Chu [19].…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Generalized Bibasic Hypergeometric Series and TheirU(n) Extensions

Bhatnagar

Milne

1997

Advances in Mathematics

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We survey summation theorems for generalized bibasic hypergeometric series found recently by Chu and perfected by Macdonald. These contain arbitrary sequences of parameters, and generalize bibasic summation theorems found by Gosper, Gasper, and Rahman. They also contain a host of matrix inversions, for infinite lower-triangular matrices, including those found by Gould, Hsu, Carlitz, and Krattenthaler. Further special cases of Krattenthaler's theorem are Andrews' matrix formulation of the Bailey Transform and Bressoud's and Gasper's inversions. We extend the telescoping arguments used for bibasic summation theorems to provide U(n+1) extensions of Gosper's and Gasper's bibasic summation theorems. Special cases include U(n+1) extensions of Carlitz's and Gasper's matrix inversions. Further specializations correspond to the U(n+1) Bailey Transform and U(n+1) Bressoud matrix inversion found previously by Milne. Applications include U(n+1) transformation and expansion formulas, and a U(n+1) extension of a q-analogue of Abel's Binomial Theorem. This q-analogue is different from those found by Jackson and Johnson.1997 Academic Press

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Section: The Factor [(And1)mentioning

confidence: 99%

Section: The Factor [(And1)mentioning

confidence: 99%