DLMF:18.12.E5 (Q5647): Difference between revisions

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Created a new Item: Wikidata Toolkit example test item creation
 
Changed an Item: Add constraint
 
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Property / constraint
 

| z | < 1 𝑧 1 {\displaystyle{\displaystyle|z|<1}}

|z|<1
Property / constraint: | z | < 1 𝑧 1 {\displaystyle{\displaystyle|z|<1}} / rank
 
Normal rank
Property / Symbols used
 
Property / Symbols used: Q11475 / rank
 
Normal rank
Property / Symbols used: Q11475 / qualifier
 
Defining formula:

C n ( λ ) ( x ) ultraspherical-Gegenbauer-polynomial 𝜆 𝑛 𝑥 {\displaystyle{\displaystyle C^{(\NVar{\lambda})}_{\NVar{n}}\left(\NVar{x}% \right)}}

\ultrasphpoly{\NVar{\lambda}}{\NVar{n}}@{\NVar{x}}
Property / Symbols used: Q11475 / qualifier
 
xml-id: C18.S3.T1.t1.r3.m2aadec
Property / Symbols used
 
Property / Symbols used: Q11750 / rank
 
Normal rank
Property / Symbols used: Q11750 / qualifier
 
Defining formula:

z 𝑧 {\displaystyle{\displaystyle z}}

z
Property / Symbols used: Q11750 / qualifier
 
xml-id: C18.S1.XMD2.m1ddec
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.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.m1ddec

Latest revision as of 15:31, 2 January 2020

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DLMF:18.12.E5
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    Statements

    1 - x z ( 1 - 2 x z + z 2 ) λ + 1 = n = 0 n + 2 λ 2 λ C n ( λ ) ( x ) z n , 1 𝑥 𝑧 superscript 1 2 𝑥 𝑧 superscript 𝑧 2 𝜆 1 superscript subscript 𝑛 0 𝑛 2 𝜆 2 𝜆 ultraspherical-Gegenbauer-polynomial 𝜆 𝑛 𝑥 superscript 𝑧 𝑛 {\displaystyle{\displaystyle\frac{1-xz}{(1-2xz+z^{2})^{\lambda+1}}=\sum_{n=0}^% {\infty}\frac{n+2\lambda}{2\lambda}C^{(\lambda)}_{n}\left(x\right)z^{n},}}
    0 references
    DLMF:18.12.E5
    0 references
    | z | < 1 𝑧 1 {\displaystyle{\displaystyle|z|<1}}
    0 references
    C n ( λ ) ( x ) ultraspherical-Gegenbauer-polynomial 𝜆 𝑛 𝑥 {\displaystyle{\displaystyle C^{(\NVar{\lambda})}_{\NVar{n}}\left(\NVar{x}% \right)}}
    C18.S3.T1.t1.r3.m2aadec
    0 references
    z 𝑧 {\displaystyle{\displaystyle z}}
    C18.S1.XMD2.m1ddec
    0 references
    n 𝑛 {\displaystyle{\displaystyle n}}
    C18.S1.XMD6.m1ddec
    0 references
    x 𝑥 {\displaystyle{\displaystyle x}}
    C18.S2.XMD3.m1ddec
    0 references