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2.3.E6

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Formula:692
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MaRDI QIDQ692

  • Label: 2.3.E6


Digital Library of Mathematical Functions ID 2.3.E6

𝒱 a , b ⁑ ( f ⁒ ( t ) ) = ∫ a b | f β€² ⁒ ( t ) ⁒ d t | ; variational-operator-on-interval π‘Ž 𝑏 𝑓 𝑑 superscript subscript π‘Ž 𝑏 superscript 𝑓 β€² 𝑑 𝑑 {\displaystyle{\displaystyle\mathcal{V}_{a,b}\left(f(t)\right)=\int_{a}^{b}|f^% {\prime}(t)\mathrm{d}t|;}}


Constraint(s)

Symbols List

  • d x π‘₯ {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}} : differential of x
  • ∫ {\displaystyle{\displaystyle\int}} : integral
  • 𝒱 a , b ⁑ ( f ) variational-operator-on-interval π‘Ž 𝑏 𝑓 {\displaystyle{\displaystyle\mathcal{V}_{\NVar{a,b}}\left(\NVar{f}\right)}} : total variation
  • a π‘Ž {\displaystyle{\displaystyle a}} : left endpoint
  • b 𝑏 {\displaystyle{\displaystyle b}} : right endpoint
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