DLMF:18.12.E1 (Q5643): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Q11750 / rank
 
Normal rank
Property / Symbols used: Q11750 / qualifier
 
test:

z 𝑧 {\displaystyle{\displaystyle z}}

z
Property / Symbols used: Q11750 / qualifier
 
xml-id: C18.S1.XMD2.m1dec
Property / Symbols used
 
Property / Symbols used: Q11726 / rank
 
Normal rank
Property / Symbols used: Q11726 / qualifier
 
test:

n 𝑛 {\displaystyle{\displaystyle n}}

n
Property / Symbols used: Q11726 / qualifier
 
xml-id: C18.S1.XMD6.m1dec
Property / Symbols used
 
Property / Symbols used: Q11727 / rank
 
Normal rank
Property / Symbols used: Q11727 / qualifier
 
test:

x 𝑥 {\displaystyle{\displaystyle x}}

x
Property / Symbols used: Q11727 / qualifier
 
xml-id: C18.S2.XMD3.m1dec

Latest revision as of 14:30, 2 January 2020

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English
DLMF:18.12.E1
No description defined

    Statements

    test
    2 α + β R ⁢ ( 1 + R - z ) α ⁢ ( 1 + R + z ) β = ∑ n = 0 ∞ P n ( α , β ) ⁡ ( x ) ⁢ z n , superscript 2 𝛼 𝛽 𝑅 superscript 1 𝑅 𝑧 𝛼 superscript 1 𝑅 𝑧 𝛽 superscript subscript 𝑛 0 Jacobi-polynomial-P 𝛼 𝛽 𝑛 𝑥 superscript 𝑧 𝑛 {\displaystyle{\displaystyle\frac{2^{\alpha+\beta}}{R(1+R-z)^{\alpha}(1+R+z)^{% \beta}}=\sum_{n=0}^{\infty}P^{(\alpha,\beta)}_{n}\left(x\right)z^{n},}}
    0 references
    DLMF id
    DLMF:18.12.E1
    0 references
    constraint
    | z | < 1 𝑧 1 {\displaystyle{\displaystyle|z|<1}}
    0 references
    Symbols used
    Q11660
    test
    P n ( α , β ) ⁡ ( x ) Jacobi-polynomial-P 𝛼 𝛽 𝑛 𝑥 {\displaystyle{\displaystyle P^{(\NVar{\alpha},\NVar{\beta})}_{\NVar{n}}\left(% \NVar{x}\right)}}
    xml-id
    C18.S3.T1.t1.r2.m2adec
    0 references
    Q11750
    test
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C18.S1.XMD2.m1dec
    0 references
    Q11726
    test
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C18.S1.XMD6.m1dec
    0 references
    Q11727
    test
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C18.S2.XMD3.m1dec
    0 references
     
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