DLMF:15.9.E6 (Q5096): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Q11661 / rank
 
Normal rank
Property / Symbols used: Q11661 / qualifier
 
test:

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: $$={{}_{2}F_{1}}\left(\NVar{a},\NVar{b};\NVar{c};\NVar{z}\right)$$ Gauss’ hypergeometric function / rank
 
Normal rank
Property / Symbols used: $$={{}_{2}F_{1}}\left(\NVar{a},\NVar{b};\NVar{c};\NVar{z}\right)$$ Gauss’ hypergeometric function / qualifier
 
test:

F ⁡ ( a , b ; c ; z ) Gauss-hypergeometric-F 𝑎 𝑏 𝑐 𝑧 {\displaystyle{\displaystyle F\left(\NVar{a},\NVar{b};\NVar{c};\NVar{z}\right)}}

\hyperF@{\NVar{a}}{\NVar{b}}{\NVar{c}}{\NVar{z}}
Property / Symbols used: $$={{}_{2}F_{1}}\left(\NVar{a},\NVar{b};\NVar{c};\NVar{z}\right)$$ Gauss’ hypergeometric function / qualifier
 
xml-id: C15.S2.E1.m2aedec
Property / Symbols used
 
Property / Symbols used: Q11649 / rank
 
Normal rank
Property / Symbols used: Q11649 / qualifier
 
test:

x 𝑥 {\displaystyle{\displaystyle x}}

x
Property / Symbols used: Q11649 / qualifier
 
xml-id: C15.S1.XMD1.m1ddec
Property / Symbols used
 
Property / Symbols used: Q11650 / rank
 
Normal rank
Property / Symbols used: Q11650 / qualifier
 
test:

n 𝑛 {\displaystyle{\displaystyle n}}

n
Property / Symbols used: Q11650 / qualifier
 
xml-id: C15.S1.XMD10.m1edec

Latest revision as of 13:08, 2 January 2020

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DLMF:15.9.E6
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    Statements

    test
    U n ⁡ ( x ) = ( n + 1 ) ⁢ F ⁡ ( - n , n + 2 3 2 ; 1 - x 2 ) . Chebyshev-polynomial-second-kind-U 𝑛 𝑥 𝑛 1 Gauss-hypergeometric-F 𝑛 𝑛 2 3 2 1 𝑥 2 {\displaystyle{\displaystyle U_{n}\left(x\right)=(n+1)F\left({-n,n+2\atop\frac% {3}{2}};\frac{1-x}{2}\right).}}
    0 references
    DLMF id
    DLMF:15.9.E6
    0 references
    Symbols used
    Q11661
    test
    U n ⁡ ( x ) Chebyshev-polynomial-second-kind-U 𝑛 𝑥 {\displaystyle{\displaystyle U_{\NVar{n}}\left(\NVar{x}\right)}}
    xml-id
    C18.S3.T1.t1.r5.m2adec
    0 references
    $$={{}_{2}F_{1}}\left(\NVar{a},\NVar{b};\NVar{c};\NVar{z}\right)$$ Gauss’ hypergeometric function
    test
    F ⁡ ( a , b ; c ; z ) Gauss-hypergeometric-F 𝑎 𝑏 𝑐 𝑧 {\displaystyle{\displaystyle F\left(\NVar{a},\NVar{b};\NVar{c};\NVar{z}\right)}}
    xml-id
    C15.S2.E1.m2aedec
    0 references
    Q11649
    test
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C15.S1.XMD1.m1ddec
    0 references
    Q11650
    test
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C15.S1.XMD10.m1edec
    0 references
     
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