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Lew, John S.; Quarles, Donald A. jun.

Nonnegative solutions of a nonlinear recurrence. (English) Zbl 0518.42029

J. Approximation Theory 38, 357-379 (1983).
Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page
scan of Zbl 0518.42029

Cited in 1 Review
Cited in 28 Documents

MSC:

42C10 Fourier series in special orthogonal functions (Legendre polynomials, Walsh functions, etc.)
65D99 Numerical approximation and computational geometry (primarily algorithms)

Keywords:

orthonormal polynomials; weight; recurrence properties; asymptotic expansion; unique nonnegative solution; computational algorithm; error estimates

Citations:

Zbl 0262.33014; Zbl 0285.33012; Zbl 0327.33008
Cite Review PDF
Full Text: DOI

References:

[1] Abramowitz, M.; Stegun, I. A., (Handbook of Mathematical Functions (1964), U. S. Gov. Printing Office: U. S. Gov. Printing Office Washington, D. C) · Zbl 0171.38503
[2] Erdélyi, A., Asymptotic Expansions (1956), Dover: Dover New York · Zbl 0070.29002
[3] Freud, G., On the greatest zero of an orthogonal polynomial, I, Acta Sci. Math. Szeged, 34, 91-97 (1973) · Zbl 0262.33014
[4] Freud, G., On the greatest zero of an orthogonal polynomial, II, Acta Sci. Math. Szeged, 36, 49-54 (1974) · Zbl 0285.33012
[5] Freud, G., On the coefficients in the recursion formulae of orthogonal polynomials, (Proc. Roy. Irish Acad. Sect. A, 76 (1976)), 1-6 · Zbl 0327.33008
[6] Goursat, E., A Course in Mathematical Analysis (1904), Ginn: Ginn New York, (E. R. Hedrick, Trans.) · JFM 35.0368.01
[7] Montel, P., Leçons sur les recurrences et leurs applications (1957), Gauthier-Villars: Gauthier-Villars Paris · Zbl 0077.06601
[8] Nevai, P. G., Polynomials orthogonal on the real line with weight \(¦x¦^α exp(−¦x¦^β)\), I\), Acta Math. Acad. Sci. Hungar., 24, 335-342 (1973), [in Russian] · Zbl 0293.33010
[10] Ortega, J. M.; Rheinboldt, W. C., Iterative Solution of Nonlinear Equations in Several Variables (1970), Academic Press: Academic Press New York · Zbl 0241.65046
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