Two \(q\)-operational equations and Hahn polynomials
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Publication:6119852
DOI10.1007/s11785-024-01496-3arXiv2210.15618MaRDI QIDQ6119852
Publication date: 25 March 2024
Published in: Complex Analysis and Operator Theory (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2210.15618
\(q\)-derivativebasic hypergeometric seriesHahn polynomials\(q\)-Gauss summation\(q\)-operational equation
(q)-calculus and related topics (05A30) Basic orthogonal polynomials and functions (Askey-Wilson polynomials, etc.) (33D45) Applications of basic hypergeometric functions (33D90)
Cites Work
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- Two operator representations for the trivariate \(q\)-polynomials and Hahn polynomials
- On Carlitz's trilinear generating functions
- Generalizations of certain Carlitz's trilinear and Srivastava-Agarwal type generating functions
- Notes on Carlitz's \(q\)-operators
- An algorithmic proof theory for hypergeometric (ordinary and ``\(q\)) multisum/integral identities
- \(q\)-differential operator identities and applications
- A \(q\)-extension of a partial differential equation and the Hahn polynomials
- Poisson kernel and multilinear generating functions of some orthogonal polynomials
- The Cauchy operator for basic hypergeometric series
- \(q\)-integral representation of the Al-Salam-Carlitz polynomials
- A q-analog of the Gauss summation theorem for hypergeometric series in U(n)
- Series inversion of some convolution transforms
- The \(q\)-harmonic oscillator and the Al-Salam and Carlitz polynomials
- On combinatorics of Al-Salam Carlitz polynomials
- Parameter augmentation for basic hypergeometric series. II
- Combinatorial proofs of Ramanujan's \(_{1} \psi_{1}\) summation and the \(q\)-Gauss summation.
- On a system of \(q\)-partial differential equations with applications to \(q\)-series
- A note on generalized \(q\)-difference equations for \(q\)-beta and Andrews-Askey integral
- Computation of Al-Salam Carlitz and Askey-Wilson moments using Motzkin paths
- Borweins' cubic theta functions revisited
- Generating functions for some families of the generalized Al-Salam-Carlitz \(q\)-polynomials
- Generalized homogeneous \(q\)-difference equations for \(q\)-polynomials and their applications to generating functions and fractional \(q\)-integrals
- \((q,c)\)-derivative operator and its applications
- Two new \(q\)-exponential operator identities and their applications
- Notes on Askey-Roy integral and certain generating functions for \(q\)-polynomials
- \(q\)-difference equation and the Cauchy operator identities
- A \(q\)-translation approach to Liu's calculus
- Orthogonality relations for Al-Salam-Carlitz polynomials of type II
- Two operator identities and their applications to terminating basic hypergeometric series and \(q\)-integrals
- New forms of the Cauchy operator and some of their applications
- An expansion of \((q, \lambda)\)-derivative operator
- On the $q$-partial differential equations and $q$-series
- Twoq-difference equations andq-operator identities
- An extension of the non-terminating6φ5summation and the Askey–Wilson polynomials
- Applications of q-Lagrange Inversion to Basic Hypergeometric Series
- CAUCHY AUGMENTATION FOR BASIC HYPERGEOMETRIC SERIES
- Invariance groups of transformations of basic hypergeometric series
- $q$-Supercongruences from the $q$-Saalschütz identity
- An extension of a supercongruence of Long and Ramakrishna
- Divided differences and well-poised q-series
- Two expansion formulas involving the Rogers–Szegő polynomials with applications
- An operator approach to the Al-Salam–Carlitz polynomials
- Some Orthogonal q‐Polynomials
- On a Transformation of Bilateral Series with Applications
- Efficient algorithms for construction of recurrence relations for the expansion and connection coefficients in series of Al-Salam–Carlitz I polynomials
- Über Orthogonalpolynome, die q‐Differenzengleichungen genügen
- On a generalized homogeneous Hahn polynomial
- A multiple \(q\)-exponential differential operational identity
- A \(q\)-operational equation and the Rogers-Szegő polynomials
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