DLMF:14.10.E3 (Q4812): Difference between revisions

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imported>Admin
 
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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.m2abdec
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.m1bdec
Property / Symbols used
 
Property / Symbols used: Q11591 / rank
 
Normal rank
Property / Symbols used: Q11591 / qualifier
 
test:

μ 𝜇 {\displaystyle{\displaystyle\mu}}

\mu
Property / Symbols used: Q11591 / qualifier
 
xml-id: C14.S1.XMD7.m1bdec
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.m1bdec

Latest revision as of 00:39, 2 January 2020

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DLMF:14.10.E3
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    Statements

    ( ν - μ + 2 ) 𝖯 ν + 2 μ ( x ) - ( 2 ν + 3 ) x 𝖯 ν + 1 μ ( x ) + ( ν + μ + 1 ) 𝖯 ν μ ( x ) = 0 , 𝜈 𝜇 2 Ferrers-Legendre-P-first-kind 𝜇 𝜈 2 𝑥 2 𝜈 3 𝑥 Ferrers-Legendre-P-first-kind 𝜇 𝜈 1 𝑥 𝜈 𝜇 1 Ferrers-Legendre-P-first-kind 𝜇 𝜈 𝑥 0 {\displaystyle{\displaystyle{(\nu-\mu+2)\mathsf{P}^{\mu}_{\nu+2}\left(x\right)% -(2\nu+3)x\mathsf{P}^{\mu}_{\nu+1}\left(x\right)}+(\nu+\mu+1)\mathsf{P}^{\mu}_% {\nu}\left(x\right)=0,}}
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    𝖯 ν μ ( x ) Ferrers-Legendre-P-first-kind 𝜇 𝜈 𝑥 {\displaystyle{\displaystyle\mathsf{P}^{\NVar{\mu}}_{\NVar{\nu}}\left(\NVar{x}% \right)}}
    C14.S3.E1.m2abdec
    0 references
    x 𝑥 {\displaystyle{\displaystyle x}}
    C14.S1.XMD1.m1bdec
    0 references
    μ 𝜇 {\displaystyle{\displaystyle\mu}}
    C14.S1.XMD7.m1bdec
    0 references
    ν 𝜈 {\displaystyle{\displaystyle\nu}}
    C14.S1.XMD8.m1bdec
    0 references