02847nam 2200601 450 991078884760332120170822144325.01-4704-0350-1(CKB)3360000000464941(EBL)3114427(SSID)ssj0000973834(PQKBManifestationID)11529962(PQKBTitleCode)TC0000973834(PQKBWorkID)10986135(PQKB)10384000(MiAaPQ)EBC3114427(RPAM)12747200(PPN)195416430(EXLCZ)99336000000046494120020418d2002 uy| 0engur|n|---|||||txtccrq-difference operators, orthogonal polynomials, and symmetric expansions /Douglas BowmanProvidence, Rhode Island :American Mathematical Society,2002.1 online resource (73 p.)Memoirs of the American Mathematical Society,0065-9266 ;number 757"Volume 159, number 757 (fourth of 5 numbers)."0-8218-2774-X Includes bibliographical references.""Contents""; ""Chapter 1. Introduction and preliminaries""; ""1.1. q-Symmetric polynomials and the q-multinomial""; ""1.2. q-Difference operators""; ""1.3. Orthogonal polynomials""; ""1.4. The symmetric functions Î?[sub(m)]""; ""1.5. Further notation, conventions and base inversion""; ""Chapter 2. New results and connections with current research""; ""2.1. Identification of Î?[sub(4)] as q-hypergeometric""; ""2.2. Symmetry creating operators""; ""2.3. Rogers's paper and orthogonal polynomials""; ""2.4. Synthesis: The continuous q-ultraspherical polynomials""""2.5. Convergence criteria for operator theorems""""2.6. A fascinating phenomenon""; ""2.7. Operator theorems and q-Heisenberg algebras""; ""Chapter 3. Vector operator identities and simple applications""; ""3.1. A new operator theorem""; ""3.2. Applications to q-series""; ""3.3. A vector q-Leibniz rule""; ""3.4. Further operator theorems and simple applications""; ""3.5. Conclusion""; ""Bibliography""Memoirs of the American Mathematical Society ;no. 757.q-seriesDifference operatorsHypergeometric functionsOrthogonal polynomialsq-series.Difference operators.Hypergeometric functions.Orthogonal polynomials.510 s515/.55Bowman Douglas1965-1566869MiAaPQMiAaPQMiAaPQBOOK9910788847603321Q-difference operators, orthogonal polynomials, and symmetric expansions3837804UNINA