LEADER 03355nam 2200589 450 001 9910788756103321 005 20170821172011.0 010 $a1-4704-0121-5 035 $a(CKB)3360000000464726 035 $a(EBL)3113977 035 $a(SSID)ssj0000889203 035 $a(PQKBManifestationID)11449087 035 $a(PQKBTitleCode)TC0000889203 035 $a(PQKBWorkID)10875858 035 $a(PQKB)10546377 035 $a(MiAaPQ)EBC3113977 035 $a(RPAM)2543043 035 $a(PPN)19541425X 035 $a(EXLCZ)993360000000464726 100 $a20140905h19951995 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aSecond-order Sturm-Liouville difference equations and orthogonal polynomials /$fAlouf Jirari 210 1$aProvidence, Rhode Island :$cAmerican Mathematical Society,$d1995. 210 4$d©1995 215 $a1 online resource (154 p.) 225 1 $aMemoirs of the American Mathematical Society,$x0065-9266 ;$vNumber 542 300 $a"January 1995, Volume 113, Number 542 (second of 4 numbers)." 311 $a0-8218-0359-X 320 $aIncludes bibliographical references. 327 $a""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"" 327 $a""3.6 Green's Function""""3.7 Self-Adjointness""; ""3.8 I?»-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"" 327 $a""Chapter 6. The Four Representative Examples""""6.1 The Generalized Tchebyshev Polynomials""; ""6.2 The Generalized Laguerre Polynomials""; ""6.3 The Krawtchouk Polynomials""; ""6.4 The Charlier Polynomials""; ""Chapter 7. Left-Definite Spaces""; ""7.1 Finite Intervals""; ""7.2 Infinite Intervals""; ""References"" 410 0$aMemoirs of the American Mathematical Society ;$vNumber 452. 606 $aSturm-Liouville equation 606 $aDifference equations 606 $aOrthogonal polynomials 615 0$aSturm-Liouville equation. 615 0$aDifference equations. 615 0$aOrthogonal polynomials. 676 $a515/.625 700 $aJirari$b Alouf$f1965-$01521082 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910788756103321 996 $aSecond-order Sturm-Liouville difference equations and orthogonal polynomials$93759982 997 $aUNINA