DLMF:14.8.E2 (Q4776): Difference between revisions

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Property / constraint
 

ν ≠ m - 1 , m - 2 , … , - m 𝜈 𝑚 1 𝑚 2 … 𝑚 {\displaystyle{\displaystyle\nu\neq m-1,m-2,\dots,-m}}

\nu\neq m-1,m-2,\dots,-m
Property / constraint: ν ≠ m - 1 , m - 2 , … , - m 𝜈 𝑚 1 𝑚 2 … 𝑚 {\displaystyle{\displaystyle\nu\neq m-1,m-2,\dots,-m}} / rank
 
Normal rank
Property / Symbols used
 
Property / Symbols used: Ferrers function of the first kind / rank
 
Normal rank
Property / Symbols used: Ferrers function of the first kind / qualifier
 
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)}}

\FerrersP[\NVar{\mu}]{\NVar{\nu}}@{\NVar{x}}
Property / Symbols used: Ferrers function of the first kind / qualifier
 
xml-id: C14.S3.E1.m2aadec
Property / Symbols used
 
Property / Symbols used: Q10759 / rank
 
Normal rank
Property / Symbols used: Q10759 / qualifier
 
test:

( a ) n Pochhammer 𝑎 𝑛 {\displaystyle{\displaystyle{\left(\NVar{a}\right)_{\NVar{n}}}}}

\Pochhammersym{\NVar{a}}{\NVar{n}}
Property / Symbols used: Q10759 / qualifier
 
xml-id: C5.S2.SS3.m1adec
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.m2aadec
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: 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.m1adec
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.m1dec
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.m1adec

Latest revision as of 00:31, 2 January 2020

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English
DLMF:14.8.E2
No description defined

    Statements

    test
    𝖯 ν m ⁡ ( x ) ∼ ( - 1 ) m ⁢ ( ν - m + 1 ) 2 ⁢ m m ! ⁢ ( 1 - x 2 ) m / 2 , asymptotically-equals Ferrers-Legendre-P-first-kind 𝑚 𝜈 𝑥 superscript 1 𝑚 Pochhammer 𝜈 𝑚 1 2 𝑚 𝑚 superscript 1 𝑥 2 𝑚 2 {\displaystyle{\displaystyle\mathsf{P}^{m}_{\nu}\left(x\right)\sim(-1)^{m}% \frac{{\left(\nu-m+1\right)_{2m}}}{m!}\left(\frac{1-x}{2}\right)^{m/2},}}
    0 references
    DLMF id
    DLMF:14.8.E2
    0 references
    constraint
    ν ≠ m - 1 , m - 2 , … , - m 𝜈 𝑚 1 𝑚 2 … 𝑚 {\displaystyle{\displaystyle\nu\neq m-1,m-2,\dots,-m}}
    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.m2aadec
    0 references
    Q10759
    test
    ( a ) n Pochhammer 𝑎 𝑛 {\displaystyle{\displaystyle{\left(\NVar{a}\right)_{\NVar{n}}}}}
    xml-id
    C5.S2.SS3.m1adec
    0 references
    asymptotic equality
    test
    ∼ asymptotically-equals {\displaystyle{\displaystyle\sim}}
    xml-id
    C2.S1.E1.m2aadec
    0 references
    Q10755
    test
    ! {\displaystyle{\displaystyle!}}
    xml-id
    introduction.Sx4.p1.t1.r15.m5adec
    0 references
    Q11589
    test
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C14.S1.XMD1.m1adec
    0 references
    Q11593
    test
    m 𝑚 {\displaystyle{\displaystyle m}}
    xml-id
    C14.S1.XMD5.m1dec
    0 references
    Q11590
    test
    ν 𝜈 {\displaystyle{\displaystyle\nu}}
    xml-id
    C14.S1.XMD8.m1adec
    0 references
     
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