References
- Bochner , S . 1929 . Über Sturm-Liouvillesche polynomsysteme . Math. Zeit. , 89 : 730 – 736 .
- Krall , HL . 1938 . Certain differential equations for Tchebysheff polynomials . Duke Math. J. , 4 : 705 – 718 .
- Krall , AM . 1980/81 . Orthogonal polynomials satisfying fourth order differential equations . Proc. R. Soc. Edinb. Sect. A , 87 : 271 – 288 .
- W.N. Everitt and L.L. Littlejohn, Orthogonal Polynomials and Spectral Theory: A Survey, Proceedings of the III International Symposium on Orthogonal Polynomials and Applications, Erice, Italy, 1990 (IMACS Ann. Comput. Appl. Math., 9 (1991), pp. 21–55).
- Koornwinder , TH . 1984 . Orthogonal polynomials with weight function (1 − x ) α (1 + x ) β + Mδ( x + 1) + Nδ( x − 1) . Canad. Math. Bull. , 27 : 205 – 214 .
- Abramowitz , M and Stegun , IA . 1992 . Handbook of Mathematical Functions with Formulae, Graphs and Mathematical Tables , New York : Dover .
- Erdélyi , A , Magnus , W , Oberhettinger , F and Tricomi , FG . 1953 . Higher Transcendental Functions , Vol. I , New York : McGraw-Hill .
- Erdélyi , A , Magnus , W , Oberhettinger , F and Tricomi , FG . 1953 . Higher Franscendental Functions , Vol. II , New York : McGraw-Hill .
- Koekoek , J and Koekoek , R . 1991 . On a differential equation for Koornwinder's generalized Laguerre polynomials . Proc. Amer. Math. Soc. , 112 : 1045 – 1054 .
- Naimark , MA . 1968 . Linear Differential Operators: II , New York : Trans. from the 2nd Russian edition, Ungar .
- Everitt , WN and Markett , C . 1994 . On a generalization of Bessel functions satisfying higher-order differential equations . J. Comput. Appl. Math. , 54 : 325 – 349 .
- Das , J , Everitt , WN , Hinton , DB , Littlejohn , LL and Markett , C . 2004 . The fourth-order Bessel-type differential equation . Appl. Anal. , 83 : 325 – 362 .
- Everitt , WN , Kalf , H , Littlejohn , LL and Markett , C . 2005 . Additional spectral properties of the fourth-order Bessel-type differential equation . Math. Nachr. , 278 : 1538 – 1549 .
- Everitt , WN , Kalf , H , Littlejohn , LL and Markett , C . 2006 . The fourth-order Bessel equation: Eigenpackets and a generalised Hankel transform . Integral Transforms Spec. Funct. , 17 : 845 – 862 .
- Everitt , WN . 2007 . Fourth-Order Bessel-Type Special Functions: A survey, Difference Equations, Special Functions and Orthogonal Polynomials pp. 189–212 (Proceedings of the International Conference, Technical University Munich, 2005, World Scientific Publishing Company, Hackensack, NJ, 2007)
- Everitt , WN and Markett , C . 2008 . Fourier-Bessel series for second-order and fourth-order Bessel differential equations . Comput. Methods Funct. Theor. , 8 : 545 – 563 .
- Everitt , WN and Markett , C . 2009 . Fourier–Bessel-type series: The fourth-order case . J. Approx. Theor. , 160 : 19 – 38 .
- W.N. Everitt, B.T. Johansson, L.L. Littlejohn, and C. Markett, Quasi-separation of the biharmonic partial differential equation, IMA J. Appl. Math. 74(5) (2009), pp. 685–709.
- W.N. Everitt, D. Smith and M. van Hoeij, The fourth-order type linear ordinary differential equations (2006). Available at arXiv.org, Mathematics, Classical Analysis and ODEs: 01 September 2006.
- Watson , GN . 1950 . A treatise on the theory of Bessel functions, , 2 , Cambridge : Cambridge University Press .
- Titchmarsh , EC . 1962 . Eigenfunction Expansions: I, , 2 , Oxford : Oxford University Press .
- Everitt , WN , Markett , C and Littlejohn , LL . 2009 . Properties of the solutions of the fourth-order Bessel-type differential equation . J. Math. Anal. Appl. , 359 : 252 – 264 .
- Everitt , WN and Kalf , H . 2007 . The Bessel differential equation and the Hankel transform . J. Comput. Appl. Math. , 208 : 3 – 19 .