DLMF:18.1.E1 (Q5486): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Q10759 / rank
 
Normal rank
Property / Symbols used: Q10759 / qualifier
 
test:

( a ) n Pochhammer 𝑎 𝑛 {\displaystyle{\displaystyle{\left(\NVar{a}\right)_{\NVar{n}}}}}

\Pochhammersym{\NVar{a}}{\NVar{n}}
Property / Symbols used: Q10759 / qualifier
 
xml-id: C5.S2.SS3.m1adec
Property / Symbols used
 
Property / Symbols used: Q10755 / rank
 
Normal rank
Property / Symbols used: Q10755 / qualifier
 
test:

! {\displaystyle{\displaystyle!}}

!
Property / Symbols used: Q10755 / qualifier
 
xml-id: introduction.Sx4.p1.t1.r15.m5adec
Property / Symbols used
 
Property / Symbols used: Q11475 / rank
 
Normal rank
Property / Symbols used: Q11475 / qualifier
 
test:

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.m2adec
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 14:12, 2 January 2020

No description defined
Language Label Description Also known as
English
DLMF:18.1.E1
No description defined

    Statements

    test
    C n ( 0 ) ⁡ ( x ) = 2 n ⁢ T n ⁡ ( x ) = 2 ⁢ ( n - 1 ) ! ( 1 2 ) n ⁢ P n ( - 1 2 , - 1 2 ) ⁡ ( x ) , ultraspherical-Gegenbauer-polynomial 0 𝑛 𝑥 2 𝑛 Chebyshev-polynomial-first-kind-T 𝑛 𝑥 2 𝑛 1 Pochhammer 1 2 𝑛 Jacobi-polynomial-P 1 2 1 2 𝑛 𝑥 {\displaystyle{\displaystyle C^{(0)}_{n}\left(x\right)=\frac{2}{n}T_{n}\left(x% \right)=\frac{2(n-1)!}{{\left(\tfrac{1}{2}\right)_{n}}}P^{(-\frac{1}{2},-\frac% {1}{2})}_{n}\left(x\right),}}
    0 references
    DLMF id
    DLMF:18.1.E1
    0 references
    constraint
    n = 1 , 2 , 3 , … 𝑛 1 2 3 … {\displaystyle{\displaystyle n=1,2,3,\dots}}
    0 references
    Symbols used
    Q11207
    test
    T n ⁡ ( x ) Chebyshev-polynomial-first-kind-T 𝑛 𝑥 {\displaystyle{\displaystyle T_{\NVar{n}}\left(\NVar{x}\right)}}
    xml-id
    C18.S3.T1.t1.r4.m2adec
    0 references
    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
    Q10759
    test
    ( a ) n Pochhammer 𝑎 𝑛 {\displaystyle{\displaystyle{\left(\NVar{a}\right)_{\NVar{n}}}}}
    xml-id
    C5.S2.SS3.m1adec
    0 references
    Q10755
    test
    ! {\displaystyle{\displaystyle!}}
    xml-id
    introduction.Sx4.p1.t1.r15.m5adec
    0 references
    Q11475
    test
    C n ( λ ) ⁡ ( x ) ultraspherical-Gegenbauer-polynomial 𝜆 𝑛 𝑥 {\displaystyle{\displaystyle C^{(\NVar{\lambda})}_{\NVar{n}}\left(\NVar{x}% \right)}}
    xml-id
    C18.S3.T1.t1.r3.m2adec
    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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