DLMF:14.2.E9 (Q4687): Difference between revisions

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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.m1hdec

Latest revision as of 01:11, 2 January 2020

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DLMF:14.2.E9
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    Statements

    Defining formula
    𝒲 ⁡ { 𝑸 ν μ ⁡ ( x ) , 𝑸 - ν - 1 μ ⁡ ( x ) } = cos ⁡ ( ν ⁢ π ) x 2 - 1 , Wronskian associated-Legendre-black-Q 𝜇 𝜈 𝑥 associated-Legendre-black-Q 𝜇 𝜈 1 𝑥 𝜈 𝜋 superscript 𝑥 2 1 {\displaystyle{\displaystyle\mathscr{W}\left\{\boldsymbol{Q}^{\mu}_{\nu}\left(% x\right),\boldsymbol{Q}^{\mu}_{-\nu-1}\left(x\right)\right\}=\frac{\cos\left(% \nu\pi\right)}{x^{2}-1},}}
    0 references
    DLMF id
    DLMF:14.2.E9
    0 references
    Symbols used
    Q10865
    Defining formula
    𝒲 Wronskian {\displaystyle{\displaystyle\mathscr{W}}}
    xml-id
    C1.S13.Px2.p1.m3aedec
    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.m3aadec
    0 references
    the ratio of the circumference of a circle to its diameter
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2abdec
    0 references
    cosine function
    Defining formula
    cos ⁡ z 𝑧 {\displaystyle{\displaystyle\cos\NVar{z}}}
    xml-id
    C4.S14.E2.m2aadec
    0 references
    Q11589
    Defining formula
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C14.S1.XMD1.m1hdec
    0 references
    Q11591
    Defining formula
    μ 𝜇 {\displaystyle{\displaystyle\mu}}
    xml-id
    C14.S1.XMD7.m1gdec
    0 references
    Q11590
    Defining formula
    ν 𝜈 {\displaystyle{\displaystyle\nu}}
    xml-id
    C14.S1.XMD8.m1hdec
    0 references
     
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