DLMF:14.23.E1 (Q4947): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: base of natural logarithm / rank
 
Normal rank
Property / Symbols used: base of natural logarithm / qualifier
 
test:

e {\displaystyle{\displaystyle\mathrm{e}}}

\expe
Property / Symbols used: base of natural logarithm / qualifier
 
xml-id: C4.S2.E11.m2adec

Revision as of 12:38, 2 January 2020

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DLMF:14.23.E1
No description defined

    Statements

    test
    P ν μ ⁡ ( x ± i ⁢ 0 ) = e ∓ μ ⁢ π ⁢ i / 2 ⁢ 𝖯 ν μ ⁡ ( x ) , Legendre-P-first-kind 𝜇 𝜈 plus-or-minus 𝑥 𝑖 0 superscript 𝑒 minus-or-plus 𝜇 𝜋 𝑖 2 Ferrers-Legendre-P-first-kind 𝜇 𝜈 𝑥 {\displaystyle{\displaystyle P^{\mu}_{\nu}\left(x\pm i0\right)=e^{\mp\mu\pi i/% 2}\mathsf{P}^{\mu}_{\nu}\left(x\right),}}
    0 references
    DLMF id
    DLMF:14.23.E1
    0 references
    Symbols used
    Ferrers function of the first kind
    test
    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.m2adec
    0 references
    Q11481
    test
    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.m1adec
    0 references
    the ratio of the circumference of a circle to its diameter
    test
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2adec
    0 references
    base of natural logarithm
    test
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2adec
    0 references
     
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