DLMF:14.21.E1 (Q4946): Difference between revisions

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imported>Admin
 
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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: Q11638 / rank
 
Normal rank
Property / Symbols used: Q11638 / qualifier
 
test:

z 𝑧 {\displaystyle{\displaystyle z}}

z
Property / Symbols used: Q11638 / qualifier
 
xml-id: C14.S1.XMD4.m1dec
Property / Symbols used
 
Property / Symbols used: Q11591 / rank
 
Normal rank
Property / Symbols used: Q11591 / qualifier
 
test:

μ 𝜇 {\displaystyle{\displaystyle\mu}}

\mu
Property / Symbols used: Q11591 / qualifier
 
xml-id: C14.S1.XMD7.m1dec
Property / Symbols used
 
Property / Symbols used: Q11590 / rank
 
Normal rank
Property / Symbols used: Q11590 / qualifier
 
test:

ν 𝜈 {\displaystyle{\displaystyle\nu}}

\nu
Property / Symbols used: Q11590 / qualifier
 
xml-id: C14.S1.XMD8.m1dec

Latest revision as of 12:38, 2 January 2020

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DLMF:14.21.E1
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    Statements

    ( 1 - z 2 ) d 2 w d z 2 - 2 z d w d z + ( ν ( ν + 1 ) - μ 2 1 - z 2 ) w = 0 . 1 superscript 𝑧 2 derivative 𝑤 𝑧 2 2 𝑧 derivative 𝑤 𝑧 𝜈 𝜈 1 superscript 𝜇 2 1 superscript 𝑧 2 𝑤 0 {\displaystyle{\displaystyle\left(1-z^{2}\right)\frac{{\mathrm{d}}^{2}w}{{% \mathrm{d}z}^{2}}-2z\frac{\mathrm{d}w}{\mathrm{d}z}+\left(\nu(\nu+1)-\frac{\mu% ^{2}}{1-z^{2}}\right)w=0.}}
    0 references
    0 references
    d f d x derivative 𝑓 𝑥 {\displaystyle{\displaystyle\frac{\mathrm{d}\NVar{f}}{\mathrm{d}\NVar{x}}}}
    C1.S4.E4.m2adec
    0 references
    z 𝑧 {\displaystyle{\displaystyle z}}
    C14.S1.XMD4.m1dec
    0 references
    μ 𝜇 {\displaystyle{\displaystyle\mu}}
    C14.S1.XMD7.m1dec
    0 references
    ν 𝜈 {\displaystyle{\displaystyle\nu}}
    C14.S1.XMD8.m1dec
    0 references