Formula:5221

Digital Library of Mathematical Functions ID 13.14.E32

${\displaystyle{\displaystyle\frac{1}{\Gamma\left(1+2\mu\right)}M_{\kappa,\mu}\left(z\right)=\frac{e^{\pm(\kappa-\mu-\frac{1}{2})\pi\mathrm{i}}}{\Gamma\left(\frac{1}{2}+\mu+\kappa\right)}W_{\kappa,\mu}\left(z\right)+\frac{e^{\pm\kappa\pi\mathrm{i}}}{\Gamma\left(\frac{1}{2}+\mu-\kappa\right)}W_{-\kappa,\mu}\left(e^{\pm\pi\mathrm{i}}z\right).}}$

Symbols List

• ${\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}$: gamma function
• ${\displaystyle{\displaystyle M_{\NVar{\kappa},\NVar{\mu}}\left(\NVar{z}\right)}}$: Whittaker confluent hypergeometric function
• ${\displaystyle{\displaystyle W_{\NVar{\kappa},\NVar{\mu}}\left(\NVar{z}\right)}}$: Whittaker confluent hypergeometric 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
• ${\displaystyle{\displaystyle z}}$: complex variable
 

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