DLMF:14.7.E10 (Q4762): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Q11602 / rank
 
Normal rank
Property / Symbols used: Q11602 / qualifier
 
Defining formula:

n 𝑛 {\displaystyle{\displaystyle n}}

n
Property / Symbols used: Q11602 / qualifier
 
xml-id: C14.S1.XMD6.m1hdec

Latest revision as of 01:29, 2 January 2020

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DLMF:14.7.E10
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    Statements

    Defining formula
    𝖯 n m ⁡ ( x ) = ( - 1 ) m + n ⁢ ( 1 - x 2 ) m / 2 2 n ⁢ n ! ⁢ d m + n d x m + n ⁡ ( 1 - x 2 ) n . Ferrers-Legendre-P-first-kind 𝑚 𝑛 𝑥 superscript 1 𝑚 𝑛 superscript 1 superscript 𝑥 2 𝑚 2 superscript 2 𝑛 𝑛 derivative 𝑥 𝑚 𝑛 superscript 1 superscript 𝑥 2 𝑛 {\displaystyle{\displaystyle\mathsf{P}^{m}_{n}\left(x\right)=(-1)^{m+n}\frac{% \left(1-x^{2}\right)^{m/2}}{2^{n}n!}\frac{{\mathrm{d}}^{m+n}}{{\mathrm{d}x}^{m% +n}}\left(1-x^{2}\right)^{n}.}}
    0 references
    DLMF id
    DLMF:14.7.E10
    0 references
    Symbols used
    Ferrers function of the first kind
    Defining formula
    𝖯 ν μ ⁡ ( x ) Ferrers-Legendre-P-first-kind 𝜇 𝜈 𝑥 {\displaystyle{\displaystyle\mathsf{P}^{\NVar{\mu}}_{\NVar{\nu}}\left(\NVar{x}% \right)}}
    xml-id
    C14.S3.E1.m2abdec
    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.m2abdec
    0 references
    Q10755
    Defining formula
    ! {\displaystyle{\displaystyle!}}
    xml-id
    introduction.Sx4.p1.t1.r15.m5abdec
    0 references
    Q11589
    Defining formula
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C14.S1.XMD1.m1idec
    0 references
    Q11593
    Defining formula
    m 𝑚 {\displaystyle{\displaystyle m}}
    xml-id
    C14.S1.XMD5.m1bdec
    0 references
    Q11602
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C14.S1.XMD6.m1hdec
    0 references
     
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