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Liouville-Green approximations for a class of linear oscillatory difference equations of the second order. (English) Zbl 0749.39001
See the preview in Zbl 0726.39002.

MSC:
39A10Additive difference equations
39A12Discrete version of topics in analysis
42C05General theory of orthogonal functions and polynomials
33C45Orthogonal polynomials and functions of hypergeometric type
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References:
[1] Ascoli, G.: Sul comportamento asintotico delle equazioni differenziali del $2{\deg}$ ordine. Rend. lincei 22, No. 6, 234-243 (1935) · Zbl 61.0489.01
[2] Bellman, R.: Stability theory of differential equations. (1953) · Zbl 0053.24705
[3] Birkhoff, G. D.: Formal theory of irregular difference equations. Acta math. 54, 205-246 (1930) · Zbl 56.0402.01
[4] Birkhoff, G. D.; Trjitzinsky, W. J.: Analytic theory of singular difference equations. Acta math. 60, 1-89 (1932) · Zbl 0006.16802
[5] Cheng, S. S.: Monotone solutions of ${\Delta}2x(k) = Q(k)x(k+1)$. Chinese J. Math. 10, 71-75 (1982) · Zbl 0491.39002
[6] Cheng, S. S.: Sturmian comparison theorems for three-term recurrence equations. J. math. Anal. appl. 111, 465-474 (1985) · Zbl 0589.39002
[7] Chihara, T. S.: An introduction to orthogonal polynomials. (1978) · Zbl 0389.33008
[8] Jha, S. W.; Máté, A.; Nevai, P.: Asymptotic for the solutions of systems of smooth recurrence equations and their applications to orthogonal polynomials. Approximation theory VI, 345-348 (1989) · Zbl 0737.41032
[9] Lakshmikantham, V.; Trigiante, D.: Theory of difference equations: numerical methods and applications. (1988) · Zbl 0683.39001
[10] Lubinsky, D. S.: The approximate approach to orthogonal polynomials for weights on (--\infty,\infty). Orthogonal polynomials: theory and practice 294, 293-310 (1990)
[11] Máté, A.; Nevai, P.: Asymptotics for solutions of smooth recurrence equations. Proc. amer. Math. soc. 93, 423-429 (1985) · Zbl 0574.42017
[12] Nevai, P.: Research problems in orthogonal polynomials. Approximation theory VI, 449-489 (1989)
[13] Olver, F. W. J.: Asymptotics and special functions. (1974) · Zbl 0303.41035
[14] Patula, W.: Growth and oscillation properties of second order linear difference equations. SIAM J. Math. anal. 10, 55-61 (1979) · Zbl 0397.39001
[15] Poincaré, H.: Sur LES équations linéaires aux différentielles et aux différences finies. Amer. J. Math. 7, 203-258 (1885) · Zbl 17.0290.01
[16] Smith, D. R.: Liouville-Green approximations via the Riccati transformation. J. math. Anal. appl. 116, 147-165 (1986) · Zbl 0618.34011
[17] Szego?, G.: Orthogonal polynomials. Amer. math. Soc. colloq. Publ. 23 (1939)
[18] Tricomi, F. G.: Vorlesungen über orthogonalreihen. (1955) · Zbl 0065.29601
[19] Van Assche, W.: Asymptotics for orthogonal polynomials and three-term recurrences. Orthogonal polynomials: theory and practice 294, 435-462 (1990) · Zbl 0697.42023
[20] Wimp, J.; Zeilberger, D.: Resurrecting the asymptotics of linear recurrences. J. math. Anal. appl. 111, 162-176 (1985) · Zbl 0579.05007
[21] Agarwal, R. P.: Difference equations and inequalities. (1991) · Zbl 0751.05008
[22] Kelley, W. G.; Peterson, A. C.: Difference equations. (1991) · Zbl 0733.39001