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  • 1 School of Mathematics, Georgia Institute of Technology, Atlanta, GA, 30332-0160, USA
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Müntz–Legendre polynomials Ln(Λ;x) associated with a sequence Λ={λk} are obtained by orthogonalizing the system in L2[0,1] with respect to the Legendre weight. Under very mild conditions on Λ, we establish the endpoint asymptotics close to x=1. The main result is
where and J0 is the Bessel function of order 0.
  • [1] Abramowitz, M. and Stegun, I. A. (Eds.), Bessel Functions Jand Y, §9.1 in Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, 9th printing, Dover (New York, 1972), pp. 358–364.

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  • [2] Borwein, P. B., Erdélyi, T. 1995 Polynomials and Polynomial Inequalities Springer New York.

  • [3] Borwein, P. B., Erdélyi, T., Zhang, J. 1994 Müntz systems and Müntz–Legendre polynomials Trans. Amer. Math. Soc. 342 523554 .

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