DLMF:14.8.E8 (Q4782): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: asymptotic equality / rank
 
Normal rank
Property / Symbols used: asymptotic equality / qualifier
 
test:

∼ asymptotically-equals {\displaystyle{\displaystyle\sim}}

\asympeq
Property / Symbols used: asymptotic equality / qualifier
 
xml-id: C2.S1.E1.m2afdec
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.m5aadec
Property / Symbols used
 
Property / Symbols used: Q11589 / rank
 
Normal rank
Property / Symbols used: Q11589 / qualifier
 
test:

x 𝑥 {\displaystyle{\displaystyle x}}

x
Property / Symbols used: Q11589 / qualifier
 
xml-id: C14.S1.XMD1.m1gdec
Property / Symbols used
 
Property / Symbols used: Q11593 / rank
 
Normal rank
Property / Symbols used: Q11593 / qualifier
 
test:

m 𝑚 {\displaystyle{\displaystyle m}}

m
Property / Symbols used: Q11593 / qualifier
 
xml-id: C14.S1.XMD5.m1adec
Property / Symbols used
 
Property / Symbols used: Q11590 / rank
 
Normal rank
Property / Symbols used: Q11590 / qualifier
 
test:

ν 𝜈 {\displaystyle{\displaystyle\nu}}

\nu
Property / Symbols used: Q11590 / qualifier
 
xml-id: C14.S1.XMD8.m1gdec

Latest revision as of 00:33, 2 January 2020

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DLMF:14.8.E8
No description defined

    Statements

    test
    P ν m ⁡ ( x ) ∼ Γ ⁡ ( ν + m + 1 ) m ! ⁢ Γ ⁡ ( ν - m + 1 ) ⁢ ( x - 1 2 ) m / 2 , asymptotically-equals Legendre-P-first-kind 𝑚 𝜈 𝑥 Euler-Gamma 𝜈 𝑚 1 𝑚 Euler-Gamma 𝜈 𝑚 1 superscript 𝑥 1 2 𝑚 2 {\displaystyle{\displaystyle P^{m}_{\nu}\left(x\right)\sim\frac{\Gamma\left(% \nu+m+1\right)}{m!\Gamma\left(\nu-m+1\right)}\left(\frac{x-1}{2}\right)^{m/2},}}
    0 references
    DLMF id
    DLMF:14.8.E8
    0 references
    constraint
    ν ± m ≠ - 1 , - 2 , - 3 , … plus-or-minus 𝜈 𝑚 1 2 3 … {\displaystyle{\displaystyle\nu\pm m\neq-1,-2,-3,\dots}}
    0 references
    Symbols used
    gamma function
    test
    Γ ⁡ ( z ) Euler-Gamma 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
    xml-id
    C5.S2.E1.m2aedec
    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.m1aadec
    0 references
    asymptotic equality
    test
    ∼ asymptotically-equals {\displaystyle{\displaystyle\sim}}
    xml-id
    C2.S1.E1.m2afdec
    0 references
    Q10755
    test
    ! {\displaystyle{\displaystyle!}}
    xml-id
    introduction.Sx4.p1.t1.r15.m5aadec
    0 references
    Q11589
    test
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C14.S1.XMD1.m1gdec
    0 references
    Q11593
    test
    m 𝑚 {\displaystyle{\displaystyle m}}
    xml-id
    C14.S1.XMD5.m1adec
    0 references
    Q11590
    test
    ν 𝜈 {\displaystyle{\displaystyle\nu}}
    xml-id
    C14.S1.XMD8.m1gdec
    0 references
     
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