Formula:6535

Digital Library of Mathematical Functions ID 18.19.E8

${\displaystyle{\displaystyle w(x)=w^{(\lambda)}(x;\phi)=\left|\Gamma\left(\lambda+\mathrm{i}x\right)\right|^{2}e^{(2\phi-\pi)x},}}$

Constraint(s)

${\displaystyle{\displaystyle 0<\phi<\pi}}$

Symbols List

• ${\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}$: gamma function
• ${\displaystyle{\displaystyle\pi}}$: the ratio of the circumference of a circle to its diameter
• ${\displaystyle{\displaystyle\mathrm{e}}}$: base of natural logarithm
• ${\displaystyle{\displaystyle\mathrm{i}}}$: imaginary unit
• ${\displaystyle{\displaystyle w(x)}}$: weight function
• ${\displaystyle{\displaystyle x}}$: real variable
 

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