DLMF:18.14.E7 (Q5670): Difference between revisions

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Property / constraint
 

0 < λ < 1 0 𝜆 1 {\displaystyle{\displaystyle 0<\lambda<1}}

0<\lambda<1
Property / constraint: 0 < λ < 1 0 𝜆 1 {\displaystyle{\displaystyle 0<\lambda<1}} / rank
 
Normal rank
Property / Symbols used
 
Property / Symbols used: gamma function / rank
 
Normal rank
Property / Symbols used: gamma function / qualifier
 
test:

Γ ( z ) Euler-Gamma 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}

\EulerGamma@{\NVar{z}}
Property / Symbols used: gamma function / qualifier
 
xml-id: C5.S2.E1.m2aadec
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.m2acdec
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.m1ddec
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.m1fdec

Latest revision as of 14:34, 2 January 2020

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DLMF:18.14.E7
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    Statements

    ( n + λ ) 1 - λ ( 1 - x 2 ) 1 2 λ | C n ( λ ) ( x ) | < 2 1 - λ Γ ( λ ) , superscript 𝑛 𝜆 1 𝜆 superscript 1 superscript 𝑥 2 1 2 𝜆 ultraspherical-Gegenbauer-polynomial 𝜆 𝑛 𝑥 superscript 2 1 𝜆 Euler-Gamma 𝜆 {\displaystyle{\displaystyle{(n+\lambda)^{1-\lambda}(1-x^{2})^{\frac{1}{2}% \lambda}|C^{(\lambda)}_{n}\left(x\right)|<\frac{2^{1-\lambda}}{\Gamma\left(% \lambda\right)}},}}
    0 references
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    0 < λ < 1 0 𝜆 1 {\displaystyle{\displaystyle 0<\lambda<1}}
    0 references
    Γ ( z ) Euler-Gamma 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
    C5.S2.E1.m2aadec
    0 references
    C n ( λ ) ( x ) ultraspherical-Gegenbauer-polynomial 𝜆 𝑛 𝑥 {\displaystyle{\displaystyle C^{(\NVar{\lambda})}_{\NVar{n}}\left(\NVar{x}% \right)}}
    C18.S3.T1.t1.r3.m2acdec
    0 references
    n 𝑛 {\displaystyle{\displaystyle n}}
    C18.S1.XMD6.m1ddec
    0 references
    x 𝑥 {\displaystyle{\displaystyle x}}
    C18.S2.XMD3.m1fdec
    0 references