DLMF:13.14.E19

MaRDI QIDQ5205

• Label: DLMF:13.14.E19

Digital Library of Mathematical Functions ID 13.14.E19

${\displaystyle{\displaystyle W_{\kappa,0}\left(z\right)=-\frac{\sqrt{z}}{\Gamma\left(\frac{1}{2}-\kappa\right)}\left(\ln z+\psi\left(\tfrac{1}{2}-\kappa\right)+2\gamma\right)+O\left(z^{\ifrac{3}{2}}\ln z\right).}}$

Symbols List

• ${\displaystyle{\displaystyle O\left(\NVar{x}\right)}}$: order not exceeding
• ${\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}$: gamma function
• ${\displaystyle{\displaystyle\gamma}}$: Euler’s constant
• ${\displaystyle{\displaystyle W_{\NVar{\kappa},\NVar{\mu}}\left(\NVar{z}\right)}}$: Whittaker confluent hypergeometric function
• ${\displaystyle{\displaystyle\psi\left(\NVar{z}\right)}}$: psi (or digamma) function
• ${\displaystyle{\displaystyle\ln\NVar{z}}}$: principal branch of logarithm function
• ${\displaystyle{\displaystyle z}}$: complex variable
 

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