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Varga, Richard S.; Carpenter, Amos J. (1987). "A conjecture of S. Bernstein in approximation theory".
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63:) on the interval by real polynomials of no more than degree
209:{\displaystyle {\frac {1}{2{\sqrt {\pi }}}}=0.28209\dots \,.}
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146:{\displaystyle \beta =\lim _{n\to \infty }2nE_{2n}(f),\,}
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was disproven by Varga and
Carpenter, who calculated
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248:{\displaystyle \beta =0.280169499023\dots \,.}
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19:, usually denoted by the Greek letter β (
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79:|, Bernstein showed that the limit
297:par des polynomes de degrés donnés"
293:"Sur la meilleure approximation de
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31:and is equal to 0.2801694990... .
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350:10.1070/SM1987v057n02ABEH003086
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48:(ƒ) be the error of the best
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29:Sergei Natanovich Bernstein
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291:Bernstein, S.N. (1914).
409:Mathematical constants
380:"Bernstein's Constant"
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50:uniform approximation
25:mathematical constant
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158:Bernstein's constant
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17:Bernstein's constant
342:1987SbMat..57..547V
164:that the limit is:
404:Numerical analysis
377:Weisstein, Eric W.
330:Math. USSR Sbornik
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398:Categories
271:(sequence
259:References
162:conjecture
35:Definition
385:MathWorld
301:Acta Math
239:…
230:β
200:…
186:π
107:∞
104:→
90:β
307:: 1–57.
23:), is a
358:0842399
338:Bibcode
277:in the
274:A073001
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39:Let
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