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DLMF:22.15.E15

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Formula:7803
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MaRDI QIDQ7803

  • Label: DLMF:22.15.E15


Digital Library of Mathematical Functions ID 22.15.E15

arccd ⁡ ( x , k ) = ∫ x 1 d t ( 1 - t 2 ) ⁢ ( 1 - k 2 ⁢ t 2 ) , inverse-Jacobi-elliptic-cd 𝑥 𝑘 superscript subscript 𝑥 1 𝑡 1 superscript 𝑡 2 1 superscript 𝑘 2 superscript 𝑡 2 {\displaystyle{\displaystyle\operatorname{arccd}\left(x,k\right)=\int_{x}^{1}% \frac{\mathrm{d}t}{\sqrt{(1-t^{2})(1-k^{2}t^{2})}},}}


Constraint(s)

- 1 ≤ x ≤ 1 1 𝑥 1 {\displaystyle{\displaystyle-1\leq x\leq 1}}

Symbols List

  • d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}} : differential of x
  • ∫ {\displaystyle{\displaystyle\int}} : integral
  • arccd ⁡ ( x , k ) inverse-Jacobi-elliptic-cd 𝑥 𝑘 {\displaystyle{\displaystyle\operatorname{arccd}\left(\NVar{x},\NVar{k}\right)}} :
  • x 𝑥 {\displaystyle{\displaystyle x}} : real
  • k 𝑘 {\displaystyle{\displaystyle k}} : modulus
  •  Edit this on Wikidata

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