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

From testwiki
Jump to navigation Jump to search
← Older edit
imported>Admin
imported>Admin
 
(7 intermediate revisions by the same user not shown)
Property / Symbols used
 
Property / Symbols used: Kelvin function / rank
 
Normal rank
Property / Symbols used: Kelvin function / qualifier
 
test:

bei ν ⁡ ( x ) Kelvin-bei 𝜈 𝑥 {\displaystyle{\displaystyle\operatorname{bei}_{\NVar{\nu}}\left(\NVar{x}% \right)}}

\Kelvinbei{\NVar{\nu}}@{\NVar{x}}
Property / Symbols used: Kelvin function / qualifier
 
xml-id: C10.S61.E1.m3aadec
Property / Symbols used
 
Property / Symbols used: Kelvin function / rank
 
Normal rank
Property / Symbols used: Kelvin function / qualifier
 
test:

ber ν ⁡ ( x ) Kelvin-ber 𝜈 𝑥 {\displaystyle{\displaystyle\operatorname{ber}_{\NVar{\nu}}\left(\NVar{x}% \right)}}

\Kelvinber{\NVar{\nu}}@{\NVar{x}}
Property / Symbols used: Kelvin function / qualifier
 
xml-id: C10.S61.E1.m2aadec
Property / Symbols used
 
Property / Symbols used: Kelvin function / rank
 
Normal rank
Property / Symbols used: Kelvin function / qualifier
 
test:

kei ν ⁡ ( x ) Kelvin-kei 𝜈 𝑥 {\displaystyle{\displaystyle\operatorname{kei}_{\NVar{\nu}}\left(\NVar{x}% \right)}}

\Kelvinkei{\NVar{\nu}}@{\NVar{x}}
Property / Symbols used: Kelvin function / qualifier
 
xml-id: C10.S61.E2.m3aadec
Property / Symbols used
 
Property / Symbols used: Kelvin function / rank
 
Normal rank
Property / Symbols used: Kelvin function / qualifier
 
test:

ker ν ⁡ ( x ) Kelvin-ker 𝜈 𝑥 {\displaystyle{\displaystyle\operatorname{ker}_{\NVar{\nu}}\left(\NVar{x}% \right)}}

\Kelvinker{\NVar{\nu}}@{\NVar{x}}
Property / Symbols used: Kelvin function / qualifier
 
xml-id: C10.S61.E2.m2aadec
Property / Symbols used
 
Property / Symbols used: derivative of $$f$$ with respect to $$x$$ / rank
 
Normal rank
Property / Symbols used: derivative of $$f$$ with respect to $$x$$ / qualifier
 
test:

d f d x derivative 𝑓 𝑥 {\displaystyle{\displaystyle\frac{\mathrm{d}\NVar{f}}{\mathrm{d}\NVar{x}}}}

\deriv{\NVar{f}}{\NVar{x}}
Property / Symbols used: derivative of $$f$$ with respect to $$x$$ / qualifier
 
xml-id: C1.S4.E4.m2adec
Property / Symbols used
 
Property / Symbols used: imaginary unit / rank
 
Normal rank
Property / Symbols used: imaginary unit / qualifier
 
test:

i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}

\iunit
Property / Symbols used: imaginary unit / qualifier
 
xml-id: C1.S9.E1.m2abdec
Property / Symbols used
 
Property / Symbols used: Q11435 / rank
 
Normal rank
Property / Symbols used: Q11435 / qualifier
 
test:

x 𝑥 {\displaystyle{\displaystyle x}}

x
Property / Symbols used: Q11435 / qualifier
 
xml-id: C10.S1.XMD4.m1bdec
Property / Symbols used
 
Property / Symbols used: Q11427 / rank
 
Normal rank
Property / Symbols used: Q11427 / qualifier
 
test:

ν 𝜈 {\displaystyle{\displaystyle\nu}}

\nu
Property / Symbols used: Q11427 / qualifier
 
xml-id: C10.S1.XMD7.m1bdec

Latest revision as of 13:20, 2 January 2020

No description defined
Language Label Description Also known as
English
DLMF:10.61.E3
No description defined

    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
    Symbols used
    Kelvin function
    test
    bei ν ⁡ ( x ) Kelvin-bei 𝜈 𝑥 {\displaystyle{\displaystyle\operatorname{bei}_{\NVar{\nu}}\left(\NVar{x}% \right)}}
    xml-id
    C10.S61.E1.m3aadec
    0 references
    Kelvin function
    test
    ber ν ⁡ ( x ) Kelvin-ber 𝜈 𝑥 {\displaystyle{\displaystyle\operatorname{ber}_{\NVar{\nu}}\left(\NVar{x}% \right)}}
    xml-id
    C10.S61.E1.m2aadec
    0 references
    Kelvin function
    test
    kei ν ⁡ ( x ) Kelvin-kei 𝜈 𝑥 {\displaystyle{\displaystyle\operatorname{kei}_{\NVar{\nu}}\left(\NVar{x}% \right)}}
    xml-id
    C10.S61.E2.m3aadec
    0 references
    Kelvin function
    test
    ker ν ⁡ ( x ) Kelvin-ker 𝜈 𝑥 {\displaystyle{\displaystyle\operatorname{ker}_{\NVar{\nu}}\left(\NVar{x}% \right)}}
    xml-id
    C10.S61.E2.m2aadec
    0 references
    derivative of $$f$$ with respect to $$x$$
    test
    d f d x derivative 𝑓 𝑥 {\displaystyle{\displaystyle\frac{\mathrm{d}\NVar{f}}{\mathrm{d}\NVar{x}}}}
    xml-id
    C1.S4.E4.m2adec
    0 references
    imaginary unit
    test
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    xml-id
    C1.S9.E1.m2abdec
    0 references
    Q11435
    test
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C10.S1.XMD4.m1bdec
    0 references
    Q11427
    test
    ν 𝜈 {\displaystyle{\displaystyle\nu}}
    xml-id
    C10.S1.XMD7.m1bdec
    0 references
     
      Retrieved from "https://lct.wmflabs.org/w/index.php?title=Item:Q3792&oldid=20302"