DLMF:14.6.E5 (Q4747): Difference between revisions

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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.m1ddec

Revision as of 01:27, 2 January 2020

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DLMF:14.6.E5
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    Statements

    Defining formula
    ( ν + 1 ) m ⁢ 𝑸 ν m ⁡ ( x ) = ( - 1 ) m ⁢ ( x 2 - 1 ) m / 2 ⁢ d m 𝑸 ν ⁡ ( x ) d x m . Pochhammer 𝜈 1 𝑚 associated-Legendre-black-Q 𝑚 𝜈 𝑥 superscript 1 𝑚 superscript superscript 𝑥 2 1 𝑚 2 derivative shorthand-associated-Legendre-black-Q 𝜈 𝑥 𝑥 𝑚 {\displaystyle{\displaystyle{\left(\nu+1\right)_{m}}\boldsymbol{Q}^{m}_{\nu}% \left(x\right)=(-1)^{m}\left(x^{2}-1\right)^{m/2}\frac{{\mathrm{d}}^{m}% \boldsymbol{Q}_{\nu}\left(x\right)}{{\mathrm{d}x}^{m}}.}}
    0 references
    DLMF id
    DLMF:14.6.E5
    0 references
    Symbols used
    Q10759
    Defining formula
    ( a ) n Pochhammer 𝑎 𝑛 {\displaystyle{\displaystyle{\left(\NVar{a}\right)_{\NVar{n}}}}}
    xml-id
    C5.S2.SS3.m1adec
    0 references
    Q11592
    Defining formula
    𝑸 ν μ ⁡ ( z ) associated-Legendre-black-Q 𝜇 𝜈 𝑧 {\displaystyle{\displaystyle\boldsymbol{Q}^{\NVar{\mu}}_{\NVar{\nu}}\left(% \NVar{z}\right)}}
    xml-id
    C14.S21.SS1.p1.m3adec
    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.m2addec
    0 references
    Q11597
    Defining formula
    𝑸 ν ⁡ ( z ) = 𝑸 ν 0 ⁡ ( z ) shorthand-associated-Legendre-black-Q 𝜈 𝑧 associated-Legendre-black-Q 0 𝜈 𝑧 {\displaystyle{\displaystyle\boldsymbol{Q}_{\NVar{\nu}}\left(\NVar{z}\right)=% \boldsymbol{Q}^{0}_{\nu}\left(z\right)}}
    xml-id
    C14.S2.SS2.p2.m6adec
    0 references
    Q11589
    Defining formula
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C14.S1.XMD1.m1ddec
    0 references
     
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