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Mathematics of Computation

Published by the American Mathematical Society since 1960 (published as Mathematical Tables and other Aids to Computation 1943-1959), Mathematics of Computation is devoted to research articles of the highest quality in computational mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.78.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

Nonexistence of Chebyshev-type quadratures on infinite intervals
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by Walter Gautschi PDF
Math. Comp. 29 (1975), 93-99 Request permission

Abstract:

Quadrature rules on semi-infinite and infinite intervals are considered involving weight functions of the Laguerre and Hermite type. It is shown that such quadrature rules cannot have equal coefficients and real nodes unless the algebraic degree of accuracy is severely limited.
References
    L. A. ANDERSON & W. GAUTSCHI, "Optimal weighted Chebyshev-type quadrature formulas" (To be published.) S. BERNSTEIN, "Sur un système d’équations indéterminées," J. Math. Pures Appl., v. 17, 1938, pp. 179-186.
  • Luigi Gatteschi, Sulla non esistenza di certe formule di quadratura, Univ. e Politec. Torino Rend. Sem. Mat. 24 (1964/65), 157–172 (Italian). MR 187394
  • V. I. Krylov, Mechanical quadratures with equal coefficients for the integrals $\int ^{\infty }_{0}$ $e^{-x}f(x)dx$ and $\int _{-\infty }\ e^{-x^{2}}f(x)dx$, Dokl. Akad. Nauk BSSR 2 (1955), 187–192 (Russian). MR 0109978
  • Herbert E. Salzer, Equally weighted quadrature formulas over semi-infinite and infinite intervals, J. Math. and Phys. 34 (1955), 54–63. MR 69586, DOI 10.1002/sapm195534154
  • Herbert S. Wilf, The possibility of Tschebycheff quadrature on infinite intervals, Proc. Nat. Acad. Sci. U.S.A. 47 (1961), 209–213. MR 125380, DOI 10.1073/pnas.47.2.209
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Additional Information
  • © Copyright 1975 American Mathematical Society
  • Journal: Math. Comp. 29 (1975), 93-99
  • MSC: Primary 65D30
  • DOI: https://doi.org/10.1090/S0025-5718-1975-0368392-3
  • MathSciNet review: 0368392