DLMF:10.61.E3 (Q3792): Difference between revisions

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Property / constraint
 

w = ber ν ⁡ x + i ⁢ bei ν ⁡ x , ber - ν ⁡ x + i ⁢ bei - ν ⁡ x ker ν ⁡ x + i ⁢ kei ν ⁡ x , ker - ν ⁡ x + i ⁢ kei - ν ⁡ x . 𝑤 Kelvin-ber 𝜈 𝑥 𝑖 Kelvin-bei 𝜈 𝑥 Kelvin-ber 𝜈 𝑥 𝑖 Kelvin-bei 𝜈 𝑥 Kelvin-ker 𝜈 𝑥 𝑖 Kelvin-kei 𝜈 𝑥 Kelvin-ker 𝜈 𝑥 𝑖 Kelvin-kei 𝜈 𝑥 {\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}}}

w=\begin{array}[t]{cc}\Kelvinber{\nu}@@{x}+i\Kelvinbei{\nu}@@{x},&\Kelvinber{-\nu}@@{x}+i\Kelvinbei{-\nu}@@{x}\\ \Kelvinker{\nu}@@{x}+i\Kelvinkei{\nu}@@{x},&\Kelvinker{-\nu}@@{x}+i\Kelvinkei{-\nu}@@{x}.\end{array}
Property / constraint: w = ber ν ⁡ x + i ⁢ bei ν ⁡ x , ber - ν ⁡ x + i ⁢ bei - ν ⁡ x ker ν ⁡ x + i ⁢ kei ν ⁡ x , ker - ν ⁡ x + i ⁢ kei - ν ⁡ x . 𝑤 Kelvin-ber 𝜈 𝑥 𝑖 Kelvin-bei 𝜈 𝑥 Kelvin-ber 𝜈 𝑥 𝑖 Kelvin-bei 𝜈 𝑥 Kelvin-ker 𝜈 𝑥 𝑖 Kelvin-kei 𝜈 𝑥 Kelvin-ker 𝜈 𝑥 𝑖 Kelvin-kei 𝜈 𝑥 {\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}}} / rank
 
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Revision as of 17:41, 30 December 2019

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DLMF:10.61.E3
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    Statements

    test
    x 2 ⁢ d 2 w d x 2 + x ⁢ d w d x - ( i ⁢ x 2 + ν 2 ) ⁢ w = 0 , superscript 𝑥 2 derivative 𝑤 𝑥 2 𝑥 derivative 𝑤 𝑥 𝑖 superscript 𝑥 2 superscript 𝜈 2 𝑤 0 {\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,}}
    0 references
    DLMF id
    DLMF:10.61.E3
    0 references
    constraint
    w = ber ν ⁡ x + i ⁢ bei ν ⁡ x , ber - ν ⁡ x + i ⁢ bei - ν ⁡ x ker ν ⁡ x + i ⁢ kei ν ⁡ x , ker - ν ⁡ x + i ⁢ kei - ν ⁡ x . 𝑤 Kelvin-ber 𝜈 𝑥 𝑖 Kelvin-bei 𝜈 𝑥 Kelvin-ber 𝜈 𝑥 𝑖 Kelvin-bei 𝜈 𝑥 Kelvin-ker 𝜈 𝑥 𝑖 Kelvin-kei 𝜈 𝑥 Kelvin-ker 𝜈 𝑥 𝑖 Kelvin-kei 𝜈 𝑥 {\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}}}
    0 references
     
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