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Formula:776

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Digital Library of Mathematical Functions ID 2.5.E30

I j ⁢ k ⁢ ( x ) = ∫ 0 ∞ f j ⁢ ( t ) ⁢ h k ⁢ ( x ⁢ t ) ⁢ d t . subscript 𝐼 𝑗 𝑘 𝑥 superscript subscript 0 subscript 𝑓 𝑗 𝑡 subscript ℎ 𝑘 𝑥 𝑡 𝑡 {\displaystyle{\displaystyle I_{jk}(x)=\int_{0}^{\infty}f_{j}(t)h_{k}(xt)% \mathrm{d}t.}}


Constraint(s)

Symbols List

  • d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}} : differential of x
  • ∫ {\displaystyle{\displaystyle\int}} : integral
  • h ⁢ ( x ) ℎ 𝑥 {\displaystyle{\displaystyle h(x)}} : locally integrable function
  • f j ⁢ ( t ) subscript 𝑓 𝑗 𝑡 {\displaystyle{\displaystyle f_{j}(t)}} : truncated functions
  • I ⁢ ( x ) 𝐼 𝑥 {\displaystyle{\displaystyle I(x)}} : convolution integral
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