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Formula:2992

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Digital Library of Mathematical Functions ID 6.12.E6

g ⁡ ( z ) = 1 z 2 ⁢ ∑ m = 0 n - 1 ( - 1 ) m ⁢ ( 2 ⁢ m + 1 ) ! z 2 ⁢ m + R n ( g ) ⁢ ( z ) , sine-cosine-integral-g 𝑧 1 superscript 𝑧 2 superscript subscript 𝑚 0 𝑛 1 superscript 1 𝑚 2 𝑚 1 superscript 𝑧 2 𝑚 superscript subscript 𝑅 𝑛 sine-cosine-integral-g 𝑧 {\displaystyle{\displaystyle\mathrm{g}\left(z\right)=\frac{1}{z^{2}}\sum_{m=0}% ^{n-1}(-1)^{m}\frac{(2m+1)!}{z^{2m}}+R_{n}^{(\mathrm{g})}(z),}}


Constraint(s)

Symbols List

  • ! {\displaystyle{\displaystyle!}} :
  • g ⁡ ( z ) sine-cosine-integral-g 𝑧 {\displaystyle{\displaystyle\mathrm{g}\left(\NVar{z}\right)}} : auxiliary function for sine and cosine integrals
  • z 𝑧 {\displaystyle{\displaystyle z}} : complex variable
  • n 𝑛 {\displaystyle{\displaystyle n}} : nonnegative integer
  • R n ( g ) ⁢ ( z ) superscript subscript 𝑅 𝑛 sine-cosine-integral-g 𝑧 {\displaystyle{\displaystyle R_{n}^{(\mathrm{g})}(z)}} : remainder term (locally)
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This page was last edited on 28 January 2024, at 10:30.
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