Previous article Next article Orthogonal Functions whose kth Derivatives are Also OrthogonalF. Max SteinF. Max Steinhttps://doi.org/10.1137/1001026PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] W. H. McEwen, Problems of closest approximation connected with the solution of linear differential equations, Trans. Amer. Math. Soc., 33 (1931), 979–997 MR1501627 0003.00801 CrossrefGoogle Scholar[2] F. Max Stein, Masters Thesis, The Approximate Solution of Integro-Differential Equations, Dissertation, The State University of Iowa, 1955 Google Scholar[3] D. C. Lewis, Orthogonal functions whose derivatives are also orthogonal, Rend. Circ. Mat. Palermo (2), 2 (1953), 159–168 (1954) MR0061194 0052.29201 CrossrefGoogle Scholar[4] Wolfgang Hahn, Über die Jacobischen Polynome und zwei verwandte Polynomklassen, Math. Z., 39 (1935), 634–638 10.1007/BF01201380 MR1545524 0011.06202 CrossrefGoogle Scholar[5] H. L. Krall, On Derivatives of Orthogonal Polynomials, Am. Math. Soc. Bull., 42 (1936), 423–428 0014.39903 CrossrefGoogle Scholar[6] M. S. Webster, Orthogonal Polynomials with Orthogonal Derivatives, Am. Math. Soc. Bull., 44 (1938), 880–887 0020.01303 CrossrefGoogle Scholar[7] Dunham Jackson, Fourier Series and Orthogonal Polynomials, Carus Monograph Series, no. 6, Mathematical Association of America, Oberlin, Ohio, 1941xii+234 MR0005912 0060.16910 CrossrefGoogle Scholar[8] I. M. Sheffer, Some properties of polynomial sets of type zero, Duke Math. J., 5 (1939), 590–622 10.1215/S0012-7094-39-00549-1 MR0000081 0022.01502 CrossrefGoogle Scholar[9] H. L. Krall and , Orrin Frink, A new class of orthogonal polynomials: The Bessel polynomials, Trans. Amer. Math. Soc., 65 (1949), 100–115 MR0028473 0031.29701 CrossrefISIGoogle Scholar[10] H. L. Krall, On derivatives of orthogonal polynomials. II, Bull. Amer. Math. Soc., 47 (1941), 261–264 MR0003854 0024.39402 CrossrefGoogle Scholar Previous article Next article FiguresRelatedReferencesCited ByDetails Classical Orthogonal PolynomialsThe Mathematica GuideBook for Symbolics Cross Ref Mathematical NotesThe American Mathematical Monthly, Vol. 70, No. 4 | 12 March 2018 Cross Ref Families of Sturm-Liouville SystemsSIAM Review, Vol. 3, No. 1 | 18 July 2006AbstractPDF (1018 KB) Volume 1, Issue 2| 1959SIAM Review History Submitted:19 February 1959Published online:18 July 2006 InformationCopyright © 1959 Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/1001026Article page range:pp. 167-170ISSN (print):0036-1445ISSN (online):1095-7200Publisher:Society for Industrial and Applied Mathematics