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Formula:2943

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Digital Library of Mathematical Functions ID 6.5.E5

Si ⁡ ( z ) = 1 2 ⁢ i ⁢ ( E 1 ⁡ ( - i ⁢ z ) - E 1 ⁡ ( i ⁢ z ) ) + 1 2 ⁢ π , sine-integral 𝑧 1 2 𝑖 exponential-integral 𝑖 𝑧 exponential-integral 𝑖 𝑧 1 2 𝜋 {\displaystyle{\displaystyle\mathrm{Si}\left(z\right)=\tfrac{1}{2}i(E_{1}\left% (-iz\right)-E_{1}\left(iz\right))+\tfrac{1}{2}\pi,}}


Constraint(s)

Symbols List

  • π {\displaystyle{\displaystyle\pi}} : the ratio of the circumference of a circle to its diameter
  • E 1 ⁡ ( z ) exponential-integral 𝑧 {\displaystyle{\displaystyle E_{1}\left(\NVar{z}\right)}} : exponential integral
  • i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}} : imaginary unit
  • Si ⁡ ( z ) sine-integral 𝑧 {\displaystyle{\displaystyle\mathrm{Si}\left(\NVar{z}\right)}} : sine integral
  • z 𝑧 {\displaystyle{\displaystyle z}} : complex variable
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