DLMF:18.7.E16 (Q5584): Difference between revisions

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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.m1odec

Revision as of 15:20, 2 January 2020

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DLMF:18.7.E16
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    Statements

    Defining formula
    C 2 ⁢ n + 1 ( λ ) ⁡ ( x ) = ( λ ) n + 1 ( 1 2 ) n + 1 ⁢ x ⁢ P n ( λ - 1 2 , 1 2 ) ⁡ ( 2 ⁢ x 2 - 1 ) . ultraspherical-Gegenbauer-polynomial 𝜆 2 𝑛 1 𝑥 Pochhammer 𝜆 𝑛 1 Pochhammer 1 2 𝑛 1 𝑥 Jacobi-polynomial-P 𝜆 1 2 1 2 𝑛 2 superscript 𝑥 2 1 {\displaystyle{\displaystyle C^{(\lambda)}_{2n+1}\left(x\right)=\frac{{\left(% \lambda\right)_{n+1}}}{{\left(\frac{1}{2}\right)_{n+1}}}xP^{(\lambda-\frac{1}{% 2},\frac{1}{2})}_{n}\left(2x^{2}-1\right).}}
    0 references
    DLMF id
    DLMF:18.7.E16
    0 references
    Symbols used
    Q11660
    Defining formula
    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.m2ajdec
    0 references
    Q10759
    Defining formula
    ( a ) n Pochhammer 𝑎 𝑛 {\displaystyle{\displaystyle{\left(\NVar{a}\right)_{\NVar{n}}}}}
    xml-id
    C5.S2.SS3.m1acdec
    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.m2aedec
    0 references
    Q11726
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C18.S1.XMD6.m1odec
    0 references
     
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