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Inversion techniques and combinatorial identities. A unified treatment for the 7F6–series identities
, 1993
"... As an extension of a useful inverse pair due to Gould–Hsu (1973), a general pair of reciprocal relations is established. The inversion technique for proving combinatorial identities, originated by Riordan (1968) and Greene & Knuth (1981), is developed systematically to explore the dual relation ..."
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relations of Pfaff–Saalschutz and Dougall–Dixon formulae. Most of the known strange hypergeometric evaluations, covered in Bailey (1935), Slater (1966), Gessel &
On formulas for π experimentally conjectured by Jauregui–Tsallis To the fine memories of Herbert Wilf (6/13/1931–1/7/2012)
, 2012
"... In a recent study of representing Dirac’s delta distribution using qexponentials, M. Jauregui and C. Tsallis experimentally discovered formulae for π as hypergeometric series as well as certain integrals. Herein, we offer rigorous proofs of these identities using various methods and our primary int ..."
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In a recent study of representing Dirac’s delta distribution using qexponentials, M. Jauregui and C. Tsallis experimentally discovered formulae for π as hypergeometric series as well as certain integrals. Herein, we offer rigorous proofs of these identities using various methods and our primary intent is to lay down an illustration of the many technical underpinnings of such evaluations. This includes an explicit discussion of creative telescoping and Carlson’s Theorem. We also generalize the Jauregui–Tsallis identities to integrals involving Chebyshev polynomials. In our pursuit, we provide an interesting tour through various topics from classical analysis to the theory of special functions.
NonAbelian quantum Hall states – exclusion statistics, Kmatrices and duality
, 2000
"... We study excitations in edge theories for nonabelian quantum Hall states, focussing on the spin polarized states proposed by Read and Rezayi and on the spin singlet states proposed by two of the authors. By studying the exclusion statistics properties of edgeelectrons and edgequasiholes, we arr ..."
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Cited by 6 (3 self)
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We study excitations in edge theories for nonabelian quantum Hall states, focussing on the spin polarized states proposed by Read and Rezayi and on the spin singlet states proposed by two of the authors. By studying the exclusion statistics properties of edgeelectrons and edgequasiholes, we arrive at a novel Kmatrix structure. Interestingly, the duality between the electron and quasihole sectors links the pseudoparticles that are characteristic for nonabelian statistics with composite particles that are associated to the ‘pairing physics’ of the nonabelian quantum Hall states.
Multidimensional Matrix Inversions And Multiple Basic Hypergeometric Series
, 1996
"... We compute the inverse of a specific infinite rdimensional matrix, thus unifying multidimensional matrix inversions recently found by Milne, Lilly, and Bhatnagar. Our inversion is an rdimensional extension of a matrix inversion previously found by Krattenthaler. We also compute the inverse of ano ..."
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Cited by 2 (1 self)
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We compute the inverse of a specific infinite rdimensional matrix, thus unifying multidimensional matrix inversions recently found by Milne, Lilly, and Bhatnagar. Our inversion is an rdimensional extension of a matrix inversion previously found by Krattenthaler. We also compute the inverse of another infinite rdimensional matrix. As applications of our matrix inversions, we derive new summation formulas for multidimensional basic hypergeometric series. We work in the setting of multiple basic hypergeometric series verywell poised on the root systems A r , C r , and D r . Our new summation formulas include D r Jackson's 8 OE 7 summations, A r and D r quadratic, and D r cubic summations. Further, we derive multivariable generalizations of Bailey's classical terminating balanced verywellpoised 10 OE 9 transformation. We obtain C r and D r 10 OE 9 transformations from an interchange of multisums, combined with A r , C r , and D r extensions of Jackson's 8 OE 7 summation. Special ...
NIST Handbook of Mathematical Functions
"... Modern developments in theoretical and applied science depend on knowledge of the properties of mathematical functions, from elementary trigonometric functions to the multitude of special functions. These functions appear whenever natural phenomena are studied, engineering problems are formulated, a ..."
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Modern developments in theoretical and applied science depend on knowledge of the properties of mathematical functions, from elementary trigonometric functions to the multitude of special functions. These functions appear whenever natural phenomena are studied, engineering problems are formulated, and numerical simulations are performed. They also crop up in statistics, financial models, and economic analysis. Using them effectively requires practitioners to have ready access to a reliable collection of their properties. This handbook results from a 10year project conducted by the National Institute of Standards and Technology with an international group of expert authors and validators. Printed in full color, it is destined to replace its predecessor, the classic but longoutdated Handbook of Mathematical Functions, edited by Abramowitz and Stegun. Included with every copy of the book is a CD with a searchable PDF.