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DLMF:29.14.E11

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Formula:9437
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MaRDI QIDQ9437

  • Label: DLMF:29.14.E11


Digital Library of Mathematical Functions ID 29.14.E11

⟨ g , h ⟩ = ∫ 0 4 ⁢ K ⁡ ∫ 0 2 ⁢ K ′ ⁡ w ⁢ ( s , t ) ⁢ g ⁢ ( s , t ) ⁢ h ⁢ ( s , t ) ⁢ d t ⁢ d s , 𝑔 ℎ superscript subscript 0 4 complete-elliptic-integral-first-kind-K 𝑘 superscript subscript 0 2 complementary-complete-elliptic-integral-first-kind-K 𝑘 𝑤 𝑠 𝑡 𝑔 𝑠 𝑡 ℎ 𝑠 𝑡 𝑡 𝑠 {\displaystyle{\displaystyle\langle g,h\rangle=\int_{0}^{4K}\!\!\int_{0}^{2{K^% {\prime}}}w(s,t)g(s,t)h(s,t)\mathrm{d}t\mathrm{d}s,}}


Constraint(s)

Symbols List

  • K ′ ⁡ ( k ) complementary-complete-elliptic-integral-first-kind-K 𝑘 {\displaystyle{\displaystyle{K^{\prime}}\left(\NVar{k}\right)}} : Legendre’s complementary complete elliptic integral of the first kind
  • K ⁡ ( k ) complete-elliptic-integral-first-kind-K 𝑘 {\displaystyle{\displaystyle K\left(\NVar{k}\right)}} : Legendre’s complete elliptic integral of the first kind
  • d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}} : differential of x
  • ∫ {\displaystyle{\displaystyle\int}} : integral
  • k 𝑘 {\displaystyle{\displaystyle k}} : real parameter
  • w ⁢ ( s , t ) 𝑤 𝑠 𝑡 {\displaystyle{\displaystyle w(s,t)}} : function
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