DLMF:14.30.E1 (Q4963): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Q10755 / rank
 
Normal rank
Property / Symbols used: Q10755 / qualifier
 
test:

! {\displaystyle{\displaystyle!}}

!
Property / Symbols used: Q10755 / qualifier
 
xml-id: introduction.Sx4.p1.t1.r15.m5adec
Property / Symbols used
 
Property / Symbols used: imaginary unit / rank
 
Normal rank
Property / Symbols used: imaginary unit / qualifier
 
test:

i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}

\iunit
Property / Symbols used: imaginary unit / qualifier
 
xml-id: C1.S9.E1.m2adec
Property / Symbols used
 
Property / Symbols used: Q11641 / rank
 
Normal rank
Property / Symbols used: Q11641 / qualifier
 
test:

m 𝑚 {\displaystyle{\displaystyle m}}

m
Property / Symbols used: Q11641 / qualifier
 
xml-id: C14.S30.XMD1.m1dec
Property / Symbols used
 
Property / Symbols used: Q11642 / rank
 
Normal rank
Property / Symbols used: Q11642 / qualifier
 
test:

l 𝑙 {\displaystyle{\displaystyle l}}

l
Property / Symbols used: Q11642 / qualifier
 
xml-id: C14.S30.XMD2.m1dec

Latest revision as of 12:43, 2 January 2020

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Language Label Description Also known as
English
DLMF:14.30.E1
No description defined

    Statements

    test
    Y l , m ⁡ ( θ , ϕ ) = ( ( l - m ) ! ⁢ ( 2 ⁢ l + 1 ) 4 ⁢ π ⁢ ( l + m ) ! ) 1 / 2 ⁢ e i ⁢ m ⁢ ϕ ⁢ 𝖯 l m ⁡ ( cos ⁡ θ ) , spherical-harmonic-Y 𝑙 𝑚 𝜃 italic-ϕ superscript 𝑙 𝑚 2 𝑙 1 4 𝜋 𝑙 𝑚 1 2 superscript 𝑒 𝑖 𝑚 italic-ϕ Ferrers-Legendre-P-first-kind 𝑚 𝑙 𝜃 {\displaystyle{\displaystyle Y_{{l},{m}}\left(\theta,\phi\right)=\left(\frac{(% l-m)!(2l+1)}{4\pi(l+m)!}\right)^{1/2}e^{im\phi}\mathsf{P}^{m}_{l}\left(\cos% \theta\right),}}
    0 references
    DLMF id
    DLMF:14.30.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
    the ratio of the circumference of a circle to its diameter
    test
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2adec
    0 references
    cosine function
    test
    cos ⁡ z 𝑧 {\displaystyle{\displaystyle\cos\NVar{z}}}
    xml-id
    C4.S14.E2.m2adec
    0 references
    base of natural logarithm
    test
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2adec
    0 references
    Q10755
    test
    ! {\displaystyle{\displaystyle!}}
    xml-id
    introduction.Sx4.p1.t1.r15.m5adec
    0 references
    imaginary unit
    test
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    xml-id
    C1.S9.E1.m2adec
    0 references
    Q11641
    test
    m 𝑚 {\displaystyle{\displaystyle m}}
    xml-id
    C14.S30.XMD1.m1dec
    0 references
    Q11642
    test
    l 𝑙 {\displaystyle{\displaystyle l}}
    xml-id
    C14.S30.XMD2.m1dec
    0 references
     
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