DLMF:18.12.E10 (Q5652): Difference between revisions

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Changed an Item: Add constraint
Changed an Item: Add constraint
 
(3 intermediate revisions by the same user not shown)
Property / Symbols used
 
Property / Symbols used: Q11661 / rank
 
Normal rank
Property / Symbols used: Q11661 / qualifier
 
Defining formula:

U n ( x ) Chebyshev-polynomial-second-kind-U 𝑛 𝑥 {\displaystyle{\displaystyle U_{\NVar{n}}\left(\NVar{x}\right)}}

\ChebyshevpolyU{\NVar{n}}@{\NVar{x}}
Property / Symbols used: Q11661 / qualifier
 
xml-id: C18.S3.T1.t1.r5.m2adec
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.m1idec
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.m1idec
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.m1hdec

Latest revision as of 15:32, 2 January 2020

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DLMF:18.12.E10
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    Statements

    1 1 - 2 x z + z 2 = n = 0 U n ( x ) z n , 1 1 2 𝑥 𝑧 superscript 𝑧 2 superscript subscript 𝑛 0 Chebyshev-polynomial-second-kind-U 𝑛 𝑥 superscript 𝑧 𝑛 {\displaystyle{\displaystyle\frac{1}{1-2xz+z^{2}}=\sum_{n=0}^{\infty}U_{n}% \left(x\right)z^{n},}}
    0 references
    DLMF:18.12.E10
    0 references
    | z | < 1 𝑧 1 {\displaystyle{\displaystyle|z|<1}}
    0 references
    U n ( x ) Chebyshev-polynomial-second-kind-U 𝑛 𝑥 {\displaystyle{\displaystyle U_{\NVar{n}}\left(\NVar{x}\right)}}
    C18.S3.T1.t1.r5.m2adec
    0 references
    z 𝑧 {\displaystyle{\displaystyle z}}
    C18.S1.XMD2.m1idec
    0 references
    n 𝑛 {\displaystyle{\displaystyle n}}
    C18.S1.XMD6.m1idec
    0 references
    x 𝑥 {\displaystyle{\displaystyle x}}
    C18.S2.XMD3.m1hdec
    0 references