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DLMF:18.19.E3

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Formula:6530
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MaRDI QIDQ6530

  • Label: DLMF:18.19.E3


Digital Library of Mathematical Functions ID 18.19.E3

w ⁢ ( x ) = w ⁢ ( x ; a , b , a ¯ , b ¯ ) = | Γ ⁡ ( a + i ⁢ x ) ⁢ Γ ⁡ ( b + i ⁢ x ) | 2 , 𝑤 𝑥 𝑤 𝑥 𝑎 𝑏 𝑎 𝑏 superscript Euler-Gamma 𝑎 imaginary-unit 𝑥 Euler-Gamma 𝑏 imaginary-unit 𝑥 2 {\displaystyle{\displaystyle w(x)=w(x;a,b,\overline{a},\overline{b})=|\Gamma% \left(a+\mathrm{i}x\right)\Gamma\left(b+\mathrm{i}x\right)|^{2},}}


Constraint(s)

Symbols List

  • Γ ⁡ ( z ) Euler-Gamma 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}} : gamma function
  • z ¯ 𝑧 {\displaystyle{\displaystyle\overline{\NVar{z}}}} : complex conjugate
  • i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}} : imaginary unit
  • w ⁢ ( x ) 𝑤 𝑥 {\displaystyle{\displaystyle w(x)}} : weight function
  • x 𝑥 {\displaystyle{\displaystyle x}} : real variable
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