03358nam 2200589 450 991048033860332120170821172011.01-4704-0121-5(CKB)3360000000464726(EBL)3113977(SSID)ssj0000889203(PQKBManifestationID)11449087(PQKBTitleCode)TC0000889203(PQKBWorkID)10875858(PQKB)10546377(MiAaPQ)EBC3113977(PPN)19541425X(EXLCZ)99336000000046472620140905h19951995 uy 0engur|n|---|||||txtccrSecond-order Sturm-Liouville difference equations and orthogonal polynomials /Alouf JirariProvidence, Rhode Island :American Mathematical Society,1995.©19951 online resource (154 p.)Memoirs of the American Mathematical Society,0065-9266 ;Number 542"January 1995, Volume 113, Number 542 (second of 4 numbers)."0-8218-0359-X Includes bibliographical references.""Table of Contents""; ""List of Figures""; ""Acknowledgements""; ""Chapter 1. Introduction""; ""1.1 The Vibrating String""; ""1.2 Network Theory""; ""1.3 Random Walk With Discrete Time Process""; ""Chapter 2. Regular Sturm-Liouville Problem""; ""2.1 Set Up""; ""2.2 Preliminary Results""; ""2.3 Orthogonality, Eigenfunction Expansion, Spectral Function, and Green's Function""; ""Chapter 3. Singular Sturm-Liouville Problem""; ""3.1 Definition""; ""3.2 C[sub(b')] Circles""; ""3.3 C[sub(a')] Circles""; ""3.4 Existence of Boundary Conditions""; ""3.5 Singular Boundary Value Problems""""3.6 Green's Function""""3.7 Self-Adjointness""; ""3.8 λ-Independence of Boundary Conditions""; ""3.9 Green's Formulas""; ""3.10 Spectral Resolution""; ""3.11 Limit-Point and Limit-Circle Tests""; ""Chapter 4. Polynomial Solutions""; ""4.1 Formal Self-Adjointness""; ""4.2 Polynomial Solutions""; ""4.3 Orthogonality of Eigenfunctions""; ""4.4 Eigenfunction Expansion""; ""Chapter 5. Polynomial Examples""; ""5.1 Classification""; ""5.2 Recurrence Relations""; ""5.3 Weight Functions and Self-Adjoint Forms""; ""5.4 Orthogonality""; ""5.5 Evaluation of the ||.||[sup(2)]""; ""5.6 Zeros""""Chapter 6. The Four Representative Examples""""6.1 The Generalized Tchebyshev Polynomials""; ""6.2 The Generalized Laguerre Polynomials""; ""6.3 The Krawtchouk Polynomials""; ""6.4 The Charlier Polynomials""; ""Chapter 7. Left-Definite Spaces""; ""7.1 Finite Intervals""; ""7.2 Infinite Intervals""; ""References""Memoirs of the American Mathematical Society ;Number 452.Sturm-Liouville equationDifference equationsOrthogonal polynomialsElectronic books.Sturm-Liouville equation.Difference equations.Orthogonal polynomials.515/.625Jirari Alouf1965-943891MiAaPQMiAaPQMiAaPQBOOK9910480338603321Second-order Sturm-Liouville difference equations and orthogonal polynomials2130663UNINA