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Proof of a conjecture of Askey on orthogonal expansions with positive coefficients


Author: William F. Trench
Journal: Bull. Amer. Math. Soc. 81 (1975), 954-956
MSC (1970): Primary 42A52, 42A56
DOI: https://doi.org/10.1090/S0002-9904-1975-13912-7
MathSciNet review: 0374798
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References [Enhancements On Off] (What's this?)

  • 1. R. Askey, Orthogonal expansions with positive coefficients, Proc. Amer. Math. Soc. 16 (1965), 1191-1194. MR 32 #2799. MR 185331
  • 2. R. Askey, Orthogonal polynomials and positivity, Studies in Appl. Math., no. 6, SIAM, Philadelphia, Pa., 1970. MR 247356
  • 3. T. J. Stieltjes, Sur les racines de l’équation 𝑋ⁿ=0, Acta Math. 9 (1887), no. 1, 385–400 (French). MR 1554723, https://doi.org/10.1007/BF02406744
  • 4. W. F. Trench, Nonnegative and alternating expansions of one set of orthogonal polynomials in terms of another, SIAM J. Math. Anal. 4 (1973), 111-115. MR 48 #4628. MR 326284
  • 5. R. S. Varga, Matrix iterative analysis, Prentioe-Hall, Englewood Cliffs, N. J., 1962. MR 28 #1725. MR 158502
  • 6. M. W. Wilson, Nonnegative expansions of polynomials, Proc. Amer. Math. Soc. 24 (1970), 100-102. MR 44 #4451. MR 287244

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DOI: https://doi.org/10.1090/S0002-9904-1975-13912-7

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