Formula:3153

Digital Library of Mathematical Functions ID 7.18.E5

${\displaystyle{\displaystyle\frac{{\mathrm{d}}^{2}W}{{\mathrm{d}z}^{2}}+2z\frac{\mathrm{d}W}{\mathrm{d}z}-2nW=0,}}$

Constraint(s)

${\displaystyle{\displaystyle W(z)=A\mathop{\mathrm{i}^{n}\mathrm{erfc}}\left(z\right)+B\mathop{\mathrm{i}^{n}\mathrm{erfc}}\left(-z\right)}}$

Symbols List

• ${\displaystyle{\displaystyle\frac{\mathrm{d}\NVar{f}}{\mathrm{d}\NVar{x}}}}$: derivative of $$f$$ with respect to $$x$$
• ${\displaystyle{\displaystyle\mathop{\mathrm{i}^{\NVar{n}}\mathrm{erfc}}\left(\NVar{z}\right)}}$: repeated integrals of the complementary error function
• ${\displaystyle{\displaystyle z}}$: complex variable
• ${\displaystyle{\displaystyle n}}$: nonnegative integer
 

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