DLMF:14.9.E13 (Q4805): Difference between revisions

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Property / constraint
 

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

\nu\neq m-1,m-2,\dots
Property / constraint: ν ≠ m - 1 , m - 2 , … 𝜈 𝑚 1 𝑚 2 … {\displaystyle{\displaystyle\nu\neq m-1,m-2,\dots}} / rank
 
Normal rank
Property / Symbols used
 
Property / Symbols used: gamma function / rank
 
Normal rank
Property / Symbols used: gamma function / qualifier
 
Defining formula:

Γ ⁡ ( z ) Euler-Gamma 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}

\EulerGamma@{\NVar{z}}
Property / Symbols used: gamma function / qualifier
 
xml-id: C5.S2.E1.m2agdec
Property / Symbols used
 
Property / Symbols used: Q11481 / rank
 
Normal rank
Property / Symbols used: Q11481 / qualifier
 
Defining formula:

P ν μ ⁡ ( z ) Legendre-P-first-kind 𝜇 𝜈 𝑧 {\displaystyle{\displaystyle P^{\NVar{\mu}}_{\NVar{\nu}}\left(\NVar{z}\right)}}

\assLegendreP[\NVar{\mu}]{\NVar{\nu}}@{\NVar{z}}
Property / Symbols used: Q11481 / qualifier
 
xml-id: C14.S21.SS1.p1.m1abdec
Property / Symbols used
 
Property / Symbols used: Q11589 / rank
 
Normal rank
Property / Symbols used: Q11589 / qualifier
 
Defining formula:

x 𝑥 {\displaystyle{\displaystyle x}}

x
Property / Symbols used: Q11589 / qualifier
 
xml-id: C14.S1.XMD1.m1ldec
Property / Symbols used
 
Property / Symbols used: Q11593 / rank
 
Normal rank
Property / Symbols used: Q11593 / qualifier
 
Defining formula:

m 𝑚 {\displaystyle{\displaystyle m}}

m
Property / Symbols used: Q11593 / qualifier
 
xml-id: C14.S1.XMD5.m1bdec
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.m1ldec

Latest revision as of 01:37, 2 January 2020

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DLMF:14.9.E13
No description defined

    Statements

    Defining formula
    P ν - m ⁡ ( x ) = Γ ⁡ ( ν - m + 1 ) Γ ⁡ ( ν + m + 1 ) ⁢ P ν m ⁡ ( x ) , Legendre-P-first-kind 𝑚 𝜈 𝑥 Euler-Gamma 𝜈 𝑚 1 Euler-Gamma 𝜈 𝑚 1 Legendre-P-first-kind 𝑚 𝜈 𝑥 {\displaystyle{\displaystyle P^{-m}_{\nu}\left(x\right)=\frac{\Gamma\left(\nu-% m+1\right)}{\Gamma\left(\nu+m+1\right)}P^{m}_{\nu}\left(x\right),}}
    0 references
    DLMF id
    DLMF:14.9.E13
    0 references
    constraint
    ν ≠ m - 1 , m - 2 , … 𝜈 𝑚 1 𝑚 2 … {\displaystyle{\displaystyle\nu\neq m-1,m-2,\dots}}
    0 references
    Symbols used
    gamma function
    Defining formula
    Γ ⁡ ( z ) Euler-Gamma 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
    xml-id
    C5.S2.E1.m2agdec
    0 references
    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.m1abdec
    0 references
    Q11589
    Defining formula
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C14.S1.XMD1.m1ldec
    0 references
    Q11593
    Defining formula
    m 𝑚 {\displaystyle{\displaystyle m}}
    xml-id
    C14.S1.XMD5.m1bdec
    0 references
    Q11590
    Defining formula
    ν 𝜈 {\displaystyle{\displaystyle\nu}}
    xml-id
    C14.S1.XMD8.m1ldec
    0 references
     
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