DLMF:18.37.E1 (Q6049): Difference between revisions

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Property / Symbols defined
 
Property / Symbols defined: disk polynomial / rank
 
Normal rank
Property / constraint
 

θ ∈ ℝ 𝜃 {\displaystyle{\displaystyle\theta\in\mathbb{R}}}

\theta\in\Reals
Property / constraint: θ ∈ ℝ 𝜃 {\displaystyle{\displaystyle\theta\in\mathbb{R}}} / rank
 
Normal rank
Property / constraint
 

θ ∈ ℝ 𝜃 ℝ {\displaystyle{\displaystyle\theta\in\mathbb{R}}}

\theta\in\mathbb{R}
Property / constraint: θ ∈ ℝ 𝜃 ℝ {\displaystyle{\displaystyle\theta\in\mathbb{R}}} / rank
 
Normal rank
Property / constraint
 

α > - 1 𝛼 1 {\displaystyle{\displaystyle\alpha>-1}}

\alpha>-1
Property / constraint: α > - 1 𝛼 1 {\displaystyle{\displaystyle\alpha>-1}} / rank
 
Normal rank
Property / Symbols used
 
Property / Symbols used: Q11660 / rank
 
Normal rank
Property / Symbols used: Q11660 / qualifier
 
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)}}

\JacobipolyP{\NVar{\alpha}}{\NVar{\beta}}{\NVar{n}}@{\NVar{x}}
Property / Symbols used: Q11660 / qualifier
 
xml-id: C18.S3.T1.t1.r2.m2adec
Property / Symbols used
 
Property / Symbols used: Q10784 / rank
 
Normal rank
Property / Symbols used: Q10784 / qualifier
 
test:

∈ {\displaystyle{\displaystyle\in}}

\in
Property / Symbols used: Q10784 / qualifier
 
xml-id: introduction.Sx4.p1.t1.r10.m2adec
Property / Symbols used
 
Property / Symbols used: base of natural logarithm / rank
 
Normal rank
Property / Symbols used: base of natural logarithm / qualifier
 
test:

e {\displaystyle{\displaystyle\mathrm{e}}}

\expe
Property / Symbols used: base of natural logarithm / qualifier
 
xml-id: C4.S2.E11.m2adec
Property / Symbols used
 
Property / Symbols used: imaginary unit / rank
 
Normal rank
Property / Symbols used: imaginary unit / qualifier
 
test:

i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}

\iunit
Property / Symbols used: imaginary unit / qualifier
 
xml-id: C1.S9.E1.m2adec
Property / Symbols used
 
Property / Symbols used: Q10812 / rank
 
Normal rank
Property / Symbols used: Q10812 / qualifier
 
test:

ℝ {\displaystyle{\displaystyle\mathbb{R}}}

\Reals
Property / Symbols used: Q10812 / qualifier
 
xml-id: introduction.Sx4.p2.t1.r14.m2adec
Property / Symbols used
 
Property / Symbols used: Q11750 / rank
 
Normal rank
Property / Symbols used: Q11750 / qualifier
 
test:

z 𝑧 {\displaystyle{\displaystyle z}}

z
Property / Symbols used: Q11750 / qualifier
 
xml-id: C18.S1.XMD2.m1dec
Property / Symbols used
 
Property / Symbols used: Q11730 / rank
 
Normal rank
Property / Symbols used: Q11730 / qualifier
 
test:

m 𝑚 {\displaystyle{\displaystyle m}}

m
Property / Symbols used: Q11730 / qualifier
 
xml-id: C18.S1.XMD5.m1dec
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

Latest revision as of 12:31, 2 January 2020

No description defined
Language Label Description Also known as
English
DLMF:18.37.E1
No description defined

    Statements

    test
    R m , n ( α ) ⁡ ( r ⁢ e i ⁢ θ ) = e i ⁢ ( m - n ) ⁢ θ ⁢ r | m - n | ⁢ P min ⁡ ( m , n ) ( α , | m - n | ) ⁡ ( 2 ⁢ r 2 - 1 ) P min ⁡ ( m , n ) ( α , | m - n | ) ⁡ ( 1 ) , disk-orthogonal-polynomial-R 𝛼 𝑚 𝑛 𝑟 superscript 𝑒 imaginary-unit 𝜃 superscript 𝑒 imaginary-unit 𝑚 𝑛 𝜃 superscript 𝑟 𝑚 𝑛 Jacobi-polynomial-P 𝛼 𝑚 𝑛 𝑚 𝑛 2 superscript 𝑟 2 1 Jacobi-polynomial-P 𝛼 𝑚 𝑛 𝑚 𝑛 1 {\displaystyle{\displaystyle R^{(\alpha)}_{m,n}\left(re^{\mathrm{i}\theta}% \right)=e^{\mathrm{i}(m-n)\theta}r^{|m-n|}\frac{P^{(\alpha,|m-n|)}_{\min(m,n)}% \left(2r^{2}-1\right)}{P^{(\alpha,|m-n|)}_{\min(m,n)}\left(1\right)},}}
    0 references
    DLMF id
    DLMF:18.37.E1
    0 references
    constraint
    θ ∈ ℝ 𝜃 {\displaystyle{\displaystyle\theta\in\mathbb{R}}}
    0 references
    θ ∈ ℝ 𝜃 ℝ {\displaystyle{\displaystyle\theta\in\mathbb{R}}}
    0 references
    α > - 1 𝛼 1 {\displaystyle{\displaystyle\alpha>-1}}
    0 references
    Symbols used
    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
    Q10784
    test
    ∈ {\displaystyle{\displaystyle\in}}
    xml-id
    introduction.Sx4.p1.t1.r10.m2adec
    0 references
    base of natural logarithm
    test
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2adec
    0 references
    imaginary unit
    test
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    xml-id
    C1.S9.E1.m2adec
    0 references
    Q10812
    test
    ℝ {\displaystyle{\displaystyle\mathbb{R}}}
    xml-id
    introduction.Sx4.p2.t1.r14.m2adec
    0 references
    Q11750
    test
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C18.S1.XMD2.m1dec
    0 references
    Q11730
    test
    m 𝑚 {\displaystyle{\displaystyle m}}
    xml-id
    C18.S1.XMD5.m1dec
    0 references
    Q11726
    test
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C18.S1.XMD6.m1dec
    0 references
     
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