DLMF:18.22.E8 (Q5876): Difference between revisions

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Changed an Item: Add constraint
Changed an Item: Add constraint
 
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Property / Symbols used
 
Property / Symbols used: Q11726 / rank
 
Normal rank
Property / Symbols used: Q11726 / qualifier
 
Defining formula:

n 𝑛 {\displaystyle{\displaystyle n}}

n
Property / Symbols used: Q11726 / qualifier
 
xml-id: C18.S1.XMD6.m1hdec
Property / Symbols used
 
Property / Symbols used: Q11731 / rank
 
Normal rank
Property / Symbols used: Q11731 / qualifier
 
Defining formula:

p n ( x ) subscript 𝑝 𝑛 𝑥 {\displaystyle{\displaystyle p_{n}(x)}}

p_{n}(x)
Property / Symbols used: Q11731 / qualifier
 
xml-id: C18.S1.XMD9.m1ddec
Property / Symbols used
 
Property / Symbols used: Q11727 / rank
 
Normal rank
Property / Symbols used: Q11727 / qualifier
 
Defining formula:

x 𝑥 {\displaystyle{\displaystyle x}}

x
Property / Symbols used: Q11727 / qualifier
 
xml-id: C18.S2.XMD3.m1fdec

Latest revision as of 01:35, 2 January 2020

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DLMF:18.22.E8
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    Statements

    ( n + 1 ) p n + 1 ( x ) = 2 ( x sin ϕ + ( n + λ ) cos ϕ ) p n ( x ) - ( n + 2 λ - 1 ) p n - 1 ( x ) . 𝑛 1 subscript 𝑝 𝑛 1 𝑥 2 𝑥 italic-ϕ 𝑛 𝜆 italic-ϕ subscript 𝑝 𝑛 𝑥 𝑛 2 𝜆 1 subscript 𝑝 𝑛 1 𝑥 {\displaystyle{\displaystyle(n+1)p_{n+1}(x)=2\left(x\sin\phi+(n+\lambda)\cos% \phi\right)p_{n}(x)-(n+2\lambda-1)p_{n-1}(x).}}
    0 references
    DLMF:18.22.E8
    0 references
    cos z 𝑧 {\displaystyle{\displaystyle\cos\NVar{z}}}
    C4.S14.E2.m2adec
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    sin z 𝑧 {\displaystyle{\displaystyle\sin\NVar{z}}}
    C4.S14.E1.m2adec
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    n 𝑛 {\displaystyle{\displaystyle n}}
    C18.S1.XMD6.m1hdec
    0 references
    p n ( x ) subscript 𝑝 𝑛 𝑥 {\displaystyle{\displaystyle p_{n}(x)}}
    C18.S1.XMD9.m1ddec
    0 references
    x 𝑥 {\displaystyle{\displaystyle x}}
    C18.S2.XMD3.m1fdec
    0 references