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Mathematics of Computation

Published by the American Mathematical Society, the Mathematics of Computation (MCOM) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Mathematics of Computation is 1.98.

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On determination of best-possible constants in integral inequalities involving derivatives
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by Beny Neta PDF
Math. Comp. 35 (1980), 1191-1193 Request permission

Abstract:

This paper is concerned with the numerical approximation of the best possible constants ${\gamma _{n,k}}$ in the inequality \[ {\left \| {{F^{(k)}}} \right \|^2} \leqslant \gamma _{n,k}^{ - 1}\;\left \{ {{{\left \| F \right \|}^2} + {{\left \| {{F^{(n)}}} \right \|}^2}} \right \},\] where \[ {\left \| F \right \|^2} = \int _0^\infty |F(x){|^2}\;dx.\] A list of all constants ${\gamma _{n,k}}$ for $n \leqslant 10$ is given.
References
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Additional Information
  • © Copyright 1980 American Mathematical Society
  • Journal: Math. Comp. 35 (1980), 1191-1193
  • MSC: Primary 26D15; Secondary 46E30, 65J99
  • DOI: https://doi.org/10.1090/S0025-5718-1980-0583496-X
  • MathSciNet review: 583496