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References
H. Bateman, The solution of linear differential equations by means of definite integrals, Trans. Cambridge Philos. Soc. 21 (1909), pp. 171–196.
A.L. Dixon and W.L. Ferrar, Infinite integrals in the theory of Bessel functions, Quart. J. Math. Oxford 1 (1930), pp. 122–145.
L. Durand, Nicholson-type integrals for products of Gegenbauer functions and related topics, in Theory and Application of Special Functions (R. Askey, ed.), Academic Press, New York, 1975, pp. 353–374.
L. Durand, Product formulas and Nicholson-type integrals for Jacobi functions. I: Summary of results, SIAM J. Anal.. 9 (1978). pp. 76–86.
Á. Elbert, Concavity of the zeros of Bessel functions, Studia Sci. Math. Hungar. 12 (1977), pp. 81–88.
Á. Elbert and A. Laforgia, On the square of the zeros of Bessel functions, SIAM J. Math. Anal. 15 (1984), pp. 206–212.
G.H. Hardy, Some formulae in the theory of Bessel functions, Proc. London Math. Soc. 23 (1925), pp. lxi–lxiii.
E.L. Ince, Ordinary Differential Equations, Longmans, London, 1927; reprinted Dover, New York, 1956.
L. Lorch and P. Szego, Higher monotonicity properties of certain Sturm-Liouville functions, Acta Math. 109 (1963), pp. 55–73.
M.E. Muldoon, A differential equations proof of a Nicholson-type formula, Z. Angew. Math. Mech. 61 (1981), pp. 598–599.
M.E. Muldoon, The variation with respect to order of zeros of Bessel functions, Rend. Sem. Mat. Univ. Politec. Torino 39 (1981), pp. 15–25.
F.W.J. Olver, Asymptotics and Special Functions, Academic Press, New York and London, 1974.
G.N. Watson, A treatise on the Theory of Bessel Functions, 2nd ed., Cambridge University Press, 1944.
J.E. Wilkins, Jr., Nicholson's integral for J 2n (z)+Y 2n (z), Bull. Amer. Math. Soc. 54 (1948), pp. 232–234.
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© 1986 Equadiff 6 and Springer-Verlag
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Muldoon, M.E. (1986). On the zeros of some special functions: Differential equations and nicholson-type formulas. In: Vosmanský, J., Zlámal, M. (eds) Equadiff 6. Lecture Notes in Mathematics, vol 1192. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0076063
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DOI: https://doi.org/10.1007/BFb0076063
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