Article PDF
Avoid common mistakes on your manuscript.
References
W. G. Bickley &J. C. P. Miller, Notes on the evaluation of zeros and turning values of Bessel functions. — V. Checks,The London, Edinburgh and Dublin Philos. Magazine and Journal of Science seventh series,36 (1945), 206–210.
I. Bihari, Oscillation and monotonity theorems concerning non-linear differential equations of the second order.Acta Math. Acad. Sci. Hungar. 9 (1958), 83–104.
N. M. Burunova,A Guide to Mathematical Tables, Supplement No. 1. English translation from the Russian, New York, 1960. (Cf. [8].)
P. J. Davis &P. Rabinowitz (a) Some geometrical theorems for abscissas and weights of Gauss type.J. Math. Anal. Appl., 2 (1961), 428–437.
— (b) Erratum,-ibid.,, 3 (1961), 619.
A. Fletcher, J. C. P. Miller, L. Rosenhead & L. J. Comrie,An Index of Mathematical Tables. 2 volumes, 2nd ed., London, 1962.
P. Hartman, On differential equations and the functionJ 2μ +Y 2μ .Amer. J. Math.,83 (1961), 154–188.
Ch. J. de La Vallée-Poussin,Cours d'Analyse Infinitésimal, vol. 1. 8th ed., Louvain, 1938, reprinted, New York, 1946.
A. V. Lebedev & R. M. Fedorova,A Guide to Mathematical Tables. English translation from the Russian, New York, 1960.
L. Lorch & L. Moser, A remark on completely monotonic sequences, with an application to summability.Canad. Math. Bull., 6 (1963).
L. Lorch & P. Szego, Monotonicity of the differences of zeros of Bessel functions as a function of order.Proc. Amer. Math. Soc. To appear.
E. Makai, On a monotonic property of certain Sturm-Liouville functions.Acta Math. Acad. Sci. Hungar., 3 (1952), 165–172.
F. W. J. Olver (editor),Royal Society Mathematical Tables, vol. 7: Bessel functions. Part III: Zeros and associated values. Cambridge, 1960.
Ch. Sturm, Memoire sur les équations différentielles du second ordre.J. Math. Pures Appl., 1 (1836), 106–186.
G. Szegö,Orthogonal Polynomials. American Mathematical Society Colloquium Publications, vol. 23, revised ed., New York, 1959.
G. N. Watson,A Treatise on the Theory of Bessel Functions. 2nd ed., Cambridge, 1944.
D. V. Widder,The Laplace Transform. Princeton, 1941.
Author information
Authors and Affiliations
Additional information
Some of this work was done a few years ago when the first-named author received partial support from the (U.S.) National Science Foundation through Research Grant NSF G-3663 to Philander Smith College, Little Rock, Arkansas. Its completion was facilitated by a grant from the University of Alberta General Research Fund. Both authors thank Professor Gabor Szegö for his interest and encouragement.
Rights and permissions
About this article
Cite this article
Lorch, L., Szego, P. Higher monotonicity properties of certain Sturm-Liouville functions. Acta Math. 109, 55–73 (1963). https://doi.org/10.1007/BF02391809
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02391809