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mathematical physics > special function > Buchstab function

mathematical analysis > functional analysis > special function > Buchstab function

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Buchstab function

The Buchstab function (or Buchstab's function) is the unique continuous function ${\\displaystyle \\omega :\\mathbb {R} _{\\geq 1}\ ightarrow \\mathbb {R} _{>0}}$ defined by the delay differential equation

${\\displaystyle \\omega (u)={\ rac {1}{u}},\\qquad \\qquad \\qquad 1\\leq u\\leq 2,}$

${\\displaystyle {\ rac {d}{du}}(u\\omega (u))=\\omega (u-1),\\qquad u\\geq 2.}$

In the second equation, the derivative at u = 2 should be taken as u approaches 2 from the right. It is named after Alexander Buchstab, who wrote about it in 1937.

(Wikipedia, The Free Encyclopedia, https://en.wikipedia.org/wiki/Buchstab_function)

fonction de Buchstab

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