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Formula:2991

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Digital Library of Mathematical Functions ID 6.12.E5

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


Constraint(s)

Symbols List

  • ! {\displaystyle{\displaystyle!}} :
  • f ⁡ ( z ) sine-cosine-integral-f 𝑧 {\displaystyle{\displaystyle\mathrm{f}\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 ( f ) ⁢ ( z ) superscript subscript 𝑅 𝑛 sine-cosine-integral-f 𝑧 {\displaystyle{\displaystyle R_{n}^{(\mathrm{f})}(z)}} : remainder term (locally)
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This page was last edited on 28 January 2024, at 10:30.
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