DLMF:14.6.E4 (Q4746): 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
 
Defining formula:

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.m2acdec
Property / Symbols used
 
Property / Symbols used: Q11448 / rank
 
Normal rank
Property / Symbols used: Q11448 / qualifier
 
Defining formula:

Q ν ⁡ ( z ) = Q ν 0 ⁡ ( z ) shorthand-Legendre-Q-second-kind 𝜈 𝑧 Legendre-Q-second-kind 0 𝜈 𝑧 {\displaystyle{\displaystyle Q_{\NVar{\nu}}\left(\NVar{z}\right)=Q^{0}_{\nu}% \left(z\right)}}

\assLegendreQ[]{\NVar{\nu}}@{\NVar{z}}=\assLegendreQ[0]{\nu}@{z}
Property / Symbols used: Q11448 / qualifier
 
xml-id: C14.S2.SS2.p2.m5adec
Property / Symbols used
 
Property / Symbols used: Q11589 / rank
 
Normal rank
Property / Symbols used: Q11589 / qualifier
 
Defining formula:

x 𝑥 {\displaystyle{\displaystyle x}}

x
Property / Symbols used: Q11589 / qualifier
 
xml-id: C14.S1.XMD1.m1cdec
Property / Symbols used
 
Property / Symbols used: Q11593 / rank
 
Normal rank
Property / Symbols used: Q11593 / qualifier
 
Defining formula:

m 𝑚 {\displaystyle{\displaystyle m}}

m
Property / Symbols used: Q11593 / qualifier
 
xml-id: C14.S1.XMD5.m1cdec
Property / Symbols used
 
Property / Symbols used: Q11590 / rank
 
Normal rank
Property / Symbols used: Q11590 / qualifier
 
Defining formula:

ν 𝜈 {\displaystyle{\displaystyle\nu}}

\nu
Property / Symbols used: Q11590 / qualifier
 
xml-id: C14.S1.XMD8.m1cdec

Latest revision as of 01:26, 2 January 2020

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DLMF:14.6.E4
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    Statements

    Defining formula
    Q ν m ⁡ ( x ) = ( x 2 - 1 ) m / 2 ⁢ d m Q ν ⁡ ( x ) d x m , Legendre-Q-second-kind 𝑚 𝜈 𝑥 superscript superscript 𝑥 2 1 𝑚 2 derivative shorthand-Legendre-Q-second-kind 𝜈 𝑥 𝑥 𝑚 {\displaystyle{\displaystyle Q^{m}_{\nu}\left(x\right)=\left(x^{2}-1\right)^{m% /2}\frac{{\mathrm{d}}^{m}Q_{\nu}\left(x\right)}{{\mathrm{d}x}^{m}},}}
    0 references
    DLMF id
    DLMF:14.6.E4
    0 references
    Symbols used
    Q11470
    Defining formula
    Q ν μ ⁡ ( z ) Legendre-Q-second-kind 𝜇 𝜈 𝑧 {\displaystyle{\displaystyle Q^{\NVar{\mu}}_{\NVar{\nu}}\left(\NVar{z}\right)}}
    xml-id
    C14.S21.SS1.p1.m2adec
    0 references
    derivative of $$f$$ with respect to $$x$$
    Defining formula
    d f d x derivative 𝑓 𝑥 {\displaystyle{\displaystyle\frac{\mathrm{d}\NVar{f}}{\mathrm{d}\NVar{x}}}}
    xml-id
    C1.S4.E4.m2acdec
    0 references
    Q11448
    Defining formula
    Q ν ⁡ ( z ) = Q ν 0 ⁡ ( z ) shorthand-Legendre-Q-second-kind 𝜈 𝑧 Legendre-Q-second-kind 0 𝜈 𝑧 {\displaystyle{\displaystyle Q_{\NVar{\nu}}\left(\NVar{z}\right)=Q^{0}_{\nu}% \left(z\right)}}
    xml-id
    C14.S2.SS2.p2.m5adec
    0 references
    Q11589
    Defining formula
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C14.S1.XMD1.m1cdec
    0 references
    Q11593
    Defining formula
    m 𝑚 {\displaystyle{\displaystyle m}}
    xml-id
    C14.S1.XMD5.m1cdec
    0 references
    Q11590
    Defining formula
    ν 𝜈 {\displaystyle{\displaystyle\nu}}
    xml-id
    C14.S1.XMD8.m1cdec
    0 references
     
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