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Higher monotonicity properties of certain Sturm-Liouville functions. (English) Zbl 0111.06502
##### Keywords:
special functions
##### References:
 [1] 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. [2] I. Bihari, Oscillation and monotonity theorems concerning non-linear differential equations of the second order.Acta Math. Acad. Sci. Hungar. 9 (1958), 83–104. · Zbl 0089.06901 · doi:10.1007/BF02023866 [3] N. M. Burunova,A Guide to Mathematical Tables, Supplement No. 1. English translation from the Russian, New York, 1960. (Cf. [8].) [4] P. J. Davis &P. Rabinowitz (a) Some geometrical theorems for abscissas and weights of Gauss type.J. Math. Anal. Appl., 2 (1961), 428–437. · Zbl 0168.14704 · doi:10.1016/0022-247X(61)90021-X [5] – (b) Erratum,-ibid.,, 3 (1961), 619. · Zbl 0107.12703 · doi:10.1016/0022-247X(61)90079-8 [6] A. Fletcher, J. C. P. Miller, L. Rosenhead & L. J. Comrie,An Index of Mathematical Tables. 2 volumes, 2nd ed., London, 1962. [7] P. Hartman, On differential equations and the functionJ $\mu$ 2 +Y $\mu$ 2 .Amer. J. Math.,83 (1961), 154–188. · Zbl 0096.27001 · doi:10.2307/2372726 [8] Ch. J. de La Vallée-Poussin,Cours d’Analyse Infinitésimal, vol. 1. 8th ed., Louvain, 1938, reprinted, New York, 1946. [9] A. V. Lebedev & R. M. Fedorova,A Guide to Mathematical Tables. English translation from the Russian, New York, 1960. [10] L. Lorch & L. Moser, A remark on completely monotonic sequences, with an application to summability.Canad. Math. Bull., 6 (1963). [11] L. Lorch & P. Szego, Monotonicity of the differences of zeros of Bessel functions as a function of order.Proc. Amer. Math. Soc. To appear. [12] E. Makai, On a monotonic property of certain Sturm-Liouville functions.Acta Math. Acad. Sci. Hungar., 3 (1952), 165–172. · Zbl 0048.32302 · doi:10.1007/BF02022519 [13] F. W. J. Olver (editor),Royal Society Mathematical Tables, vol. 7: Bessel functions. Part III: Zeros and associated values. Cambridge, 1960. [14] Ch. Sturm, Memoire sur les équations différentielles du second ordre.J. Math. Pures Appl., 1 (1836), 106–186. [15] G. Szegö,Orthogonal Polynomials. American Mathematical Society Colloquium Publications, vol. 23, revised ed., New York, 1959. [16] G. N. Watson,A Treatise on the Theory of Bessel Functions. 2nd ed., Cambridge, 1944. [17] D. V. Widder,The Laplace Transform. Princeton, 1941.