MINIMAL DEGREES OF GENOCCHI-PEANO FUNCTIONS: CALCULUS MOTIVATED NUMBER THEORETICAL ESTIMATES

Krzysztof Chris Ciesielski

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MINIMAL DEGREES OF GENOCCHI-PEANO FUNCTIONS: CALCULUS MOTIVATED NUMBER THEORETICAL ESTIMATES

机译：Genocchi-Peano函数的最小度：计算的动因数理论估计

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A rational function of the form (x_1~(α_1)x_2~(α_2)...x_n~(α_n))/(x_1~(β_1)+x_2~(β_2)...x_n~(β_n))-is a Genocchi-Peano example. GPE. provided it is discontinuous, but its restriction to any hyperplane is continuous. We show that the minimal degree D(n) of a GPE of n-variables equals 2 [(e~2)/(e~2-1)n]+2i for some i ∈ {0, 1, 2}. We also investigate the minimal degree D_b(n) of a bounded GPE of n-variables and note that D(n) < D_b(n) ≤ n(n + 1). Finding better bounds for numbers D_b(n) remains an open problem.

机译：形式（x_1〜（α_1）x_2〜（α_2）... x_n〜（α_n））/（x_1〜（β_1）+ x_2〜（β_2）... x_n〜（β_n））-的有理函数是Genocchi-Peano的例子。 GPE。如果它是不连续的，但对任何超平面的限制是连续的。我们表明，对于某些i∈{0，1，2}，n个变量的GPE的最小程度D（n）等于2 [（（e〜2）/（e〜2-1）n] + 2i）。我们还研究了n个变量的有界GPE的最小度D_b（n），并注意D（n）

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来源
《Real analysis exchange》 |2018年第2期|281-292|共12页
作者
Krzysztof Chris Ciesielski;
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作者单位

Department of Mathematics, West Virginia University, Morgantown, WV 26506-6310,Department of Radiology, MIPG, University of Pennsylvania, Philadelphia, PA 19104-6021;

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正文语种 eng
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关键词
separate continuity; hyperplane continuity; smallest degree; Genocchi-Peano examples;

机译：单独的连续性;超平面连续性最小度Genocchi-Peano的例子;

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MINIMAL DEGREES OF GENOCCHI-PEANO FUNCTIONS: CALCULUS MOTIVATED NUMBER THEORETICAL ESTIMATES

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