DLMF:14.18.E9 (Q4910): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Q11245 / rank
 
Normal rank
Property / Symbols used: Q11245 / qualifier
 
test:

∉ {\displaystyle{\displaystyle\notin}}

\notin
Property / Symbols used: Q11245 / qualifier
 
xml-id: introduction.Sx4.p1.t1.r11.m2aadec
Property / Symbols used
 
Property / Symbols used: sine function / rank
 
Normal rank
Property / Symbols used: sine function / qualifier
 
test:

sin ⁡ z 𝑧 {\displaystyle{\displaystyle\sin\NVar{z}}}

\sin@@{\NVar{z}}
Property / Symbols used: sine function / qualifier
 
xml-id: C4.S14.E1.m2addec
Property / Symbols used
 
Property / Symbols used: Q11602 / rank
 
Normal rank
Property / Symbols used: Q11602 / qualifier
 
test:

n 𝑛 {\displaystyle{\displaystyle n}}

n
Property / Symbols used: Q11602 / qualifier
 
xml-id: C14.S1.XMD6.m1ddec
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.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.m1edec

Latest revision as of 12:29, 2 January 2020

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English
DLMF:14.18.E9
No description defined

    Statements

    test
    𝖯 ν - μ ⁡ ( x ) = sin ⁡ ( ν ⁢ π ) π ⁢ ∑ n = 0 ∞ ( - 1 ) n ⁢ 2 ⁢ n + 1 ( ν - n ) ⁢ ( ν + n + 1 ) ⁢ 𝖯 n - μ ⁡ ( x ) , Ferrers-Legendre-P-first-kind 𝜇 𝜈 𝑥 𝜈 𝜋 𝜋 superscript subscript 𝑛 0 superscript 1 𝑛 2 𝑛 1 𝜈 𝑛 𝜈 𝑛 1 Ferrers-Legendre-P-first-kind 𝜇 𝑛 𝑥 {\displaystyle{\displaystyle\mathsf{P}^{-\mu}_{\nu}\left(x\right)=\frac{\sin% \left(\nu\pi\right)}{\pi}\sum_{n=0}^{\infty}(-1)^{n}\frac{2n+1}{(\nu-n)(\nu+n+% 1)}\mathsf{P}^{-\mu}_{n}\left(x\right),}}
    0 references
    DLMF id
    DLMF:14.18.E9
    0 references
    constraint
    ν ∉ ℤ 𝜈 {\displaystyle{\displaystyle\nu\notin\mathbb{Z}}}
    0 references
    μ ≥ 0 𝜇 0 {\displaystyle{\displaystyle\mu\geq 0}}
    0 references
    ν ∉ ℤ 𝜈 ℤ {\displaystyle{\displaystyle\nu\notin\mathbb{Z}}}
    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.m2acdec
    0 references
    the ratio of the circumference of a circle to its diameter
    test
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2aadec
    0 references
    Q10818
    test
    ℤ {\displaystyle{\displaystyle\mathbb{Z}}}
    xml-id
    introduction.Sx4.p2.t1.r20.m2aadec
    0 references
    Q11245
    test
    ∉ {\displaystyle{\displaystyle\notin}}
    xml-id
    introduction.Sx4.p1.t1.r11.m2aadec
    0 references
    sine function
    test
    sin ⁡ z 𝑧 {\displaystyle{\displaystyle\sin\NVar{z}}}
    xml-id
    C4.S14.E1.m2addec
    0 references
    Q11602
    test
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C14.S1.XMD6.m1ddec
    0 references
    Q11591
    test
    μ 𝜇 {\displaystyle{\displaystyle\mu}}
    xml-id
    C14.S1.XMD7.m1dec
    0 references
    Q11590
    test
    ν 𝜈 {\displaystyle{\displaystyle\nu}}
    xml-id
    C14.S1.XMD8.m1edec
    0 references
     
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