DLMF:14.24.E3 (Q4956): 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.m1bdec

Revision as of 13:41, 2 January 2020

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DLMF:14.24.E3
No description defined

    Statements

    Defining formula
    P ν , s - μ ⁡ ( z ) = e s ⁢ μ ⁢ π ⁢ i ⁢ P ν - μ ⁡ ( z ) , Legendre-P-first-kind 𝜇 𝜈 𝑠 𝑧 superscript 𝑒 𝑠 𝜇 𝜋 𝑖 Legendre-P-first-kind 𝜇 𝜈 𝑧 {\displaystyle{\displaystyle P^{-\mu}_{\nu,s}\left(z\right)=e^{s\mu\pi i}P^{-% \mu}_{\nu}\left(z\right),}}
    0 references
    DLMF id
    DLMF:14.24.E3
    0 references
    Symbols used
    Q11481
    Defining formula
    P ν μ ⁡ ( z ) Legendre-P-first-kind 𝜇 𝜈 𝑧 {\displaystyle{\displaystyle P^{\NVar{\mu}}_{\NVar{\nu}}\left(\NVar{z}\right)}}
    xml-id
    C14.S21.SS1.p1.m1aadec
    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
    base of natural logarithm
    Defining formula
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2abdec
    0 references
    imaginary unit
    Defining formula
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    xml-id
    C1.S9.E1.m2abdec
    0 references
    Q11638
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C14.S1.XMD4.m1bdec
    0 references
    Q11591
    Defining formula
    μ 𝜇 {\displaystyle{\displaystyle\mu}}
    xml-id
    C14.S1.XMD7.m1bdec
    0 references
    Q11590
    Defining formula
    ν 𝜈 {\displaystyle{\displaystyle\nu}}
    xml-id
    C14.S1.XMD8.m1bdec
    0 references
     
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