Formula:4489

Digital Library of Mathematical Functions ID 10.61.E3

${\displaystyle{\displaystyle x^{2}\frac{{\mathrm{d}}^{2}w}{{\mathrm{d}x}^{2}}+x\frac{\mathrm{d}w}{\mathrm{d}x}-(ix^{2}+\nu^{2})w=0,}}$

Constraint(s)

${\displaystyle{\displaystyle w=\begin{array}[t]{cc}\operatorname{ber}_{\nu}x+i\operatorname{bei}_{\nu}x,&\operatorname{ber}_{-\nu}x+i\operatorname{bei}_{-\nu}x\\ \operatorname{ker}_{\nu}x+i\operatorname{kei}_{\nu}x,&\operatorname{ker}_{-\nu}x+i\operatorname{kei}_{-\nu}x.\end{array}}}$

Symbols List

• ${\displaystyle{\displaystyle\operatorname{bei}_{\NVar{\nu}}\left(\NVar{x}\right)}}$: Kelvin function
• ${\displaystyle{\displaystyle\operatorname{ber}_{\NVar{\nu}}\left(\NVar{x}\right)}}$: Kelvin function
• ${\displaystyle{\displaystyle\operatorname{kei}_{\NVar{\nu}}\left(\NVar{x}\right)}}$: Kelvin function
• ${\displaystyle{\displaystyle\operatorname{ker}_{\NVar{\nu}}\left(\NVar{x}\right)}}$: Kelvin function
• ${\displaystyle{\displaystyle\frac{\mathrm{d}\NVar{f}}{\mathrm{d}\NVar{x}}}}$: derivative of $$f$$ with respect to $$x$$
• ${\displaystyle{\displaystyle\mathrm{i}}}$: imaginary unit
• ${\displaystyle{\displaystyle x}}$: real variable
• ${\displaystyle{\displaystyle\nu}}$: complex parameter
 

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