Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
F.V. ATKINSON AND W.N. EVERITT, "Orthogonal polynomials which satisfy second order differential equations", in E.B. Christoffel, ed. P.L. Butzer and F. Fehér, Birkhäuser, Basel, 1981, 173–181.
R.P. BOAS, JR, "The Stieltjes moment problem for functions of bounded variation", Bull. Amer. Math. Soc., 45, 1939, 399–404.
S. BOCHNER, "Über Sturm-Liouvillesche Polynomsysteme", Math. Z. 29, 1929, 730–736.
T.H. KOORNWINDER, "Orthogonal polynomials with weight function (1−x)α(1+x)β + Mδ(x+1) + Nδ(x−1)", Canad. Math. Bull., 27(2), 1984, 205–214.
H.L. KRALL, "Certain differential equations for Tchebycheff polynomials", Duke Math. J., 4, 1938, 705–718.
H.L. KRALL, "On orthogonal polynomials satisfying a certain fourth order equation", The Pennsylvania State College Studies, No. 6, The Pennsylvania State College, State College, Pa., 1940.
H.L. KRALL and O. FRINK, "A new class of orthogonal polynomials: the Bessel polynomials", Trans. Amer. Math. Soc., 65, 1969, 100–115.
H.L. KRALL and I.M. SHEFFER, "Orthogonal polynomials in two variables", Ann. Mat. Pura Appl., 4, 1967, 325–376.
A.M. KRALL and R.D. MORTON, "Distributional weight functions for orthogonal polynomials", SIAM J. Math. Anal., 9, 1978, 604–626.
A.M. KRALL, "Orthogonal polynomials satisfying fourth order differential equations", Proc. Roy. Soc. Edinburgh Sect. A, 87, 1981, 271–288.
A.M. KRALL and L.L. LITTLEJOHN, "Orthogonal polynomials and singular Sturm-Liouville systems I", Rocky Mountain J. Math., 16(3), 1986, 435–479.
A.M. KRALL and L.L. LITTLEJOHN. "Orthogonal polynomials and singular Sturm-Liouville systems II", submitted.
A.M. KRALL and L.L. LITTLEJOHN, "Sturm-Liouville operators and orthogonal polynomials", submitted.
L.L. LITTLEJOHN, "The Krall polynomials: a new class of orthogonal polynomials", Quaestiones Math., 5, 1982, 255–265.
L.L. LITTLEJOHN, "On the classification of differential equations having orthogonal polynomial solutions", Ann. Mat. Pura Appl., 4, 1984, 35–53.
L.L. LITTLEJOHN, "An application of a new theorem on orthogonal polynomials and differential equations", Quaestiones Math., 10, 1986, 49–61.
L.L. LITTLEJOHN and A.M. KRALL, "On the classification of differential equations having orthogonal polynomial solutions II", Ann. Mat. Pura Appl., to appear.
L.L. LITTLEJOHN and A.M. KRALL, "Necessary and sufficient conditions for the existence of symmetry factors for real ordinary differential expressions", submitted.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1988 Springer-Verlag
About this paper
Cite this paper
Littlejohn, L.L. (1988). Orthogonal polynomial solutions to ordinary and partial differential equations. In: Alfaro, M., Dehesa, J.S., Marcellan, F.J., Rubio de Francia, J.L., Vinuesa, J. (eds) Orthogonal Polynomials and their Applications. Lecture Notes in Mathematics, vol 1329. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0083355
Download citation
DOI: https://doi.org/10.1007/BFb0083355
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-19489-7
Online ISBN: 978-3-540-39295-8
eBook Packages: Springer Book Archive