DLMF:12.2.E18

MaRDI QIDQ4800

• Label: DLMF:12.2.E18

Digital Library of Mathematical Functions ID 12.2.E18

${\displaystyle{\displaystyle\sqrt{2\pi}U\left(a,z\right)=\Gamma\left(\tfrac{1}{2}-a\right)\left(e^{\mp i\pi(\frac{1}{2}a+\frac{1}{4})}U\left(-a,\pm iz\right)+e^{\pm i\pi(\frac{1}{2}a+\frac{1}{4})}U\left(-a,\mp iz\right)\right),}}$

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
• ${\displaystyle{\displaystyle U\left(\NVar{a},\NVar{z}\right)}}$:
• ${\displaystyle{\displaystyle z}}$: complex variable
• ${\displaystyle{\displaystyle a}}$: real or complex parameter
 

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