DLMF:18.14.E6 (Q5669): Difference between revisions

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‎Changed an Item: Add constraint
‎Changed an Item: Add constraint
 
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Property / Symbols used
 
Property / Symbols used: Q10759 / rank
 
Normal rank
Property / Symbols used: Q10759 / qualifier
 
Defining formula:

( 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.m1addec
Property / Symbols used
 
Property / Symbols used: Q10755 / rank
 
Normal rank
Property / Symbols used: Q10755 / qualifier
 
Defining formula:

! {\displaystyle{\displaystyle!}}

!
Property / Symbols used: Q10755 / qualifier
 
xml-id: introduction.Sx4.p1.t1.r15.m5aedec
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.m2abdec
Property / Symbols used
 
Property / Symbols used: Q11730 / rank
 
Normal rank
Property / Symbols used: Q11730 / qualifier
 
Defining formula:

m 𝑚 {\displaystyle{\displaystyle m}}

m
Property / Symbols used: Q11730 / qualifier
 
xml-id: C18.S1.XMD5.m1adec
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.m1edec

Latest revision as of 15:34, 2 January 2020

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Language Label Description Also known as
English
DLMF:18.14.E6
No description defined

    Statements

    Defining formula
    | C 2 ⁢ m + 1 ( λ ) ⁡ ( x ) | < - 2 ⁢ ( λ ) m + 1 ( ( 2 ⁢ m + 1 ) ⁢ ( 2 ⁢ λ + 2 ⁢ m + 1 ) ) 1 2 ⁢ m ! , ultraspherical-Gegenbauer-polynomial 𝜆 2 𝑚 1 𝑥 2 Pochhammer 𝜆 𝑚 1 superscript 2 𝑚 1 2 𝜆 2 𝑚 1 1 2 𝑚 {\displaystyle{\displaystyle|C^{(\lambda)}_{2m+1}\left(x\right)|<\frac{-2{% \left(\lambda\right)_{m+1}}}{\left((2m+1)(2\lambda+2m+1)\right)^{\frac{1}{2}}m% !},}}
    0 references
    DLMF id
    DLMF:18.14.E6
    0 references
    constraint
    - 1 2 < λ < 0 1 2 𝜆 0 {\displaystyle{\displaystyle-\tfrac{1}{2}<\lambda<0}}
    0 references
    Symbols used
    Q10759
    Defining formula
    ( a ) n Pochhammer 𝑎 𝑛 {\displaystyle{\displaystyle{\left(\NVar{a}\right)_{\NVar{n}}}}}
    xml-id
    C5.S2.SS3.m1addec
    0 references
    Q10755
    Defining formula
    ! {\displaystyle{\displaystyle!}}
    xml-id
    introduction.Sx4.p1.t1.r15.m5aedec
    0 references
    Q11475
    Defining formula
    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.m2abdec
    0 references
    Q11730
    Defining formula
    m 𝑚 {\displaystyle{\displaystyle m}}
    xml-id
    C18.S1.XMD5.m1adec
    0 references
    Q11727
    Defining formula
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C18.S2.XMD3.m1edec
    0 references
     
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