Formula:5244

Digital Library of Mathematical Functions ID 13.15.E22

${\displaystyle{\displaystyle\frac{{\mathrm{d}}^{n}}{{\mathrm{d}z}^{n}}\left(e^{\frac{1}{2}z}z^{\mu-\frac{1}{2}}W_{\kappa,\mu}\left(z\right)\right)=(-1)^{n}{\left(\tfrac{1}{2}-\mu-\kappa\right)_{n}}e^{\frac{1}{2}z}z^{\mu-\frac{1}{2}(n+1)}\*W_{\kappa-\frac{1}{2}n,\mu-\frac{1}{2}n}\left(z\right),}}$

Symbols List

• ${\displaystyle{\displaystyle{\left(\NVar{a}\right)_{\NVar{n}}}}}$:
• ${\displaystyle{\displaystyle W_{\NVar{\kappa},\NVar{\mu}}\left(\NVar{z}\right)}}$: Whittaker confluent hypergeometric function
• ${\displaystyle{\displaystyle\frac{\mathrm{d}\NVar{f}}{\mathrm{d}\NVar{x}}}}$: derivative of $$f$$ with respect to $$x$$
• ${\displaystyle{\displaystyle\mathrm{e}}}$: base of natural logarithm
• ${\displaystyle{\displaystyle n}}$: nonnegative integer
• ${\displaystyle{\displaystyle z}}$: complex variable
 

Resources that cite this formula

No records found.