DLMF:29.2.E4 (Q8577): Difference between revisions

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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.m2abdec
Property / Symbols used
 
Property / Symbols used: sine function / rank
 
Normal rank
Property / Symbols used: sine function / qualifier
 
test:

sin ⁡ z 𝑧 {\displaystyle{\displaystyle\sin\NVar{z}}}

\sin@@{\NVar{z}}
Property / Symbols used: sine function / qualifier
 
xml-id: C4.S14.E1.m2adec
Property / Symbols used
 
Property / Symbols used: Q12349 / rank
 
Normal rank
Property / Symbols used: Q12349 / qualifier
 
test:

h ℎ {\displaystyle{\displaystyle h}}

h
Property / Symbols used: Q12349 / qualifier
 
xml-id: C29.S1.XMD7.m1bdec
Property / Symbols used
 
Property / Symbols used: Q12350 / rank
 
Normal rank
Property / Symbols used: Q12350 / qualifier
 
test:

k 𝑘 {\displaystyle{\displaystyle k}}

k
Property / Symbols used: Q12350 / qualifier
 
xml-id: C29.S1.XMD8.m1ddec
Property / Symbols used
 
Property / Symbols used: Q12351 / rank
 
Normal rank
Property / Symbols used: Q12351 / qualifier
 
test:

ν 𝜈 {\displaystyle{\displaystyle\nu}}

\nu
Property / Symbols used: Q12351 / qualifier
 
xml-id: C29.S1.XMD9.m1bdec
Property / Symbols used
 
Property / Symbols used: change of variable (locally) / rank
 
Normal rank
Property / Symbols used: change of variable (locally) / qualifier
 
test:

ϕ italic-ϕ {\displaystyle{\displaystyle\phi}}

\phi
Property / Symbols used: change of variable (locally) / qualifier
 
xml-id: C29.S2.XMD3.m1dec

Latest revision as of 14:42, 2 January 2020

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DLMF:29.2.E4
No description defined

    Statements

    test
    ( 1 - k 2 ⁢ cos 2 ⁡ ϕ ) ⁢ d 2 w d ϕ 2 + k 2 ⁢ cos ⁡ ϕ ⁢ sin ⁡ ϕ ⁢ d w d ϕ + ( h - ν ⁢ ( ν + 1 ) ⁢ k 2 ⁢ cos 2 ⁡ ϕ ) ⁢ w = 0 , 1 superscript 𝑘 2 2 italic-ϕ derivative 𝑤 italic-ϕ 2 superscript 𝑘 2 italic-ϕ italic-ϕ derivative 𝑤 italic-ϕ ℎ 𝜈 𝜈 1 superscript 𝑘 2 2 italic-ϕ 𝑤 0 {\displaystyle{\displaystyle(1-k^{2}{\cos^{2}}\phi)\frac{{\mathrm{d}}^{2}w}{{% \mathrm{d}\phi}^{2}}+k^{2}\cos\phi\sin\phi\frac{\mathrm{d}w}{\mathrm{d}\phi}+(% h-\nu(\nu+1)k^{2}{\cos^{2}}\phi)w=0,}}
    0 references
    DLMF id
    DLMF:29.2.E4
    0 references
    Symbols used
    cosine function
    test
    cos ⁡ z 𝑧 {\displaystyle{\displaystyle\cos\NVar{z}}}
    xml-id
    C4.S14.E2.m2adec
    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.m2abdec
    0 references
    sine function
    test
    sin ⁡ z 𝑧 {\displaystyle{\displaystyle\sin\NVar{z}}}
    xml-id
    C4.S14.E1.m2adec
    0 references
    Q12349
    test
    h ℎ {\displaystyle{\displaystyle h}}
    xml-id
    C29.S1.XMD7.m1bdec
    0 references
    Q12350
    test
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C29.S1.XMD8.m1ddec
    0 references
    Q12351
    test
    ν 𝜈 {\displaystyle{\displaystyle\nu}}
    xml-id
    C29.S1.XMD9.m1bdec
    0 references
    change of variable (locally)
    test
    ϕ italic-ϕ {\displaystyle{\displaystyle\phi}}
    xml-id
    C29.S2.XMD3.m1dec
    0 references
     
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