DLMF:18.16.E7 (Q5730): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Q10784 / rank
 
Normal rank
Property / Symbols used: Q10784 / qualifier
 
Defining formula:

∈ {\displaystyle{\displaystyle\in}}

\in
Property / Symbols used: Q10784 / qualifier
 
xml-id: introduction.Sx4.p1.t1.r10.m2aedec
Property / Symbols used
 
Property / Symbols used: Q11169 / rank
 
Normal rank
Property / Symbols used: Q11169 / qualifier
 
Defining formula:

⌊ x ⌋ 𝑥 {\displaystyle{\displaystyle\left\lfloor\NVar{x}\right\rfloor}}

\floor{\NVar{x}}
Property / Symbols used: Q11169 / qualifier
 
xml-id: introduction.Sx4.p1.t1.r17.m4abdec
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.m1edec
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.m1fdec
Property / Symbols used
 
Property / Symbols used: DLMF:18.15.E5 / rank
 
Normal rank
Property / Symbols used: DLMF:18.15.E5 / qualifier
 
Defining formula:

ρ 𝜌 {\displaystyle{\displaystyle\rho}}

\rho
Property / Symbols used: DLMF:18.15.E5 / qualifier
 
xml-id: C18.S15.XMD4.m1bdec
Property / Symbols used
 
Property / Symbols used: Q11760 / rank
 
Normal rank
Property / Symbols used: Q11760 / qualifier
 
Defining formula:

θ n , m subscript 𝜃 𝑛 𝑚 {\displaystyle{\displaystyle\theta_{n,m}}}

\theta_{n,m}
Property / Symbols used: Q11760 / qualifier
 
xml-id: C18.S16.XMD1.m1fdec

Latest revision as of 15:42, 2 January 2020

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English
DLMF:18.16.E7
No description defined

    Statements

    Defining formula
    θ n , m ≥ j α , m ( ρ 2 + 1 4 - 1 2 ⁢ ( α 2 + β 2 ) - π - 2 ⁢ ( 1 - 4 ⁢ α 2 ) ) 1 2 , subscript 𝜃 𝑛 𝑚 subscript 𝑗 𝛼 𝑚 superscript superscript 𝜌 2 1 4 1 2 superscript 𝛼 2 superscript 𝛽 2 superscript 𝜋 2 1 4 superscript 𝛼 2 1 2 {\displaystyle{\displaystyle\theta_{n,m}\geq\frac{j_{\alpha,m}}{\left(\rho^{2}% +\tfrac{1}{4}-\tfrac{1}{2}(\alpha^{2}+\beta^{2})-\pi^{-2}(1-4\alpha^{2})\right% )^{\frac{1}{2}}},}}
    0 references
    DLMF id
    DLMF:18.16.E7
    0 references
    comment
    Warning: Falling back to standard tex;
    0 references
    constraint
    m = 1 , 2 , … , ⌊ 1 2 ⁢ n ⌋ 𝑚 1 2 … 1 2 𝑛 {\displaystyle{\displaystyle m=1,2,\dots,\left\lfloor\tfrac{1}{2}n\right% \rfloor}}
    0 references
    α , β ∈ [ - 1 2 , 1 2 ] 𝛼 𝛽 1 2 1 2 {\displaystyle{\displaystyle\alpha,\beta\in[-\tfrac{1}{2},\tfrac{1}{2}]}}
    0 references
    m = 1 , 2 , … , ⌊ 1 2 ⁢ n ⌋ 𝑚 1 2 … 1 2 𝑛 {\displaystyle{\displaystyle m=1,2,\dots,\left\lfloor\tfrac{1}{2}n\right% \rfloor}}
    0 references
    Symbols used
    the ratio of the circumference of a circle to its diameter
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2aedec
    0 references
    Q10815
    Defining formula
    [ a , b ] 𝑎 𝑏 {\displaystyle{\displaystyle[\NVar{a},\NVar{b}]}}
    xml-id
    introduction.Sx4.p1.t1.r30.m6addec
    0 references
    Q10784
    Defining formula
    ∈ {\displaystyle{\displaystyle\in}}
    xml-id
    introduction.Sx4.p1.t1.r10.m2aedec
    0 references
    Q11169
    Defining formula
    ⌊ x ⌋ 𝑥 {\displaystyle{\displaystyle\left\lfloor\NVar{x}\right\rfloor}}
    xml-id
    introduction.Sx4.p1.t1.r17.m4abdec
    0 references
    Q11730
    Defining formula
    m 𝑚 {\displaystyle{\displaystyle m}}
    xml-id
    C18.S1.XMD5.m1edec
    0 references
    Q11726
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C18.S1.XMD6.m1fdec
    0 references
    DLMF:18.15.E5
    Defining formula
    ρ 𝜌 {\displaystyle{\displaystyle\rho}}
    xml-id
    C18.S15.XMD4.m1bdec
    0 references
    Q11760
    Defining formula
    θ n , m subscript 𝜃 𝑛 𝑚 {\displaystyle{\displaystyle\theta_{n,m}}}
    xml-id
    C18.S16.XMD1.m1fdec
    0 references
     
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