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Higher monotonicity properties of certain Sturm-Liouville functions. (English) Zbl 0111.06502
References:
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[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
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[7]P. Hartman, On differential equations and the functionJ μ 2 +Y μ 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.