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Formula:3002

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Digital Library of Mathematical Functions ID 6.14.E6

∫ 0 ∞ Ci 2 ⁡ ( t ) ⁢ d t = ∫ 0 ∞ si 2 ⁡ ( t ) ⁢ d t = 1 2 ⁢ π , superscript subscript 0 cosine-integral 2 𝑡 𝑡 superscript subscript 0 shifted-sine-integral 2 𝑡 𝑡 1 2 𝜋 {\displaystyle{\displaystyle\int_{0}^{\infty}{\mathrm{Ci}^{2}}\left(t\right)% \mathrm{d}t=\int_{0}^{\infty}{\mathrm{si}^{2}}\left(t\right)\mathrm{d}t=\tfrac% {1}{2}\pi,}}


Constraint(s)

Symbols List

  • π {\displaystyle{\displaystyle\pi}} : the ratio of the circumference of a circle to its diameter
  • Ci ⁡ ( z ) cosine-integral 𝑧 {\displaystyle{\displaystyle\mathrm{Ci}\left(\NVar{z}\right)}} : cosine integral
  • d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}} : differential of x
  • ∫ {\displaystyle{\displaystyle\int}} : integral
  • si ⁡ ( z ) shifted-sine-integral 𝑧 {\displaystyle{\displaystyle\mathrm{si}\left(\NVar{z}\right)}} : sine integral
  •  Edit this on Wikidata

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