DLMF:18.16.E5 (Q5728): Difference between revisions

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Property / constraint
 

α ∈ ( - 1 2 , 1 2 ) 𝛼 1 2 1 2 {\displaystyle{\displaystyle\alpha\in(-\tfrac{1}{2},\tfrac{1}{2})}}

\alpha\in(-\tfrac{1}{2},\tfrac{1}{2})
Property / constraint: α ∈ ( - 1 2 , 1 2 ) 𝛼 1 2 1 2 {\displaystyle{\displaystyle\alpha\in(-\tfrac{1}{2},\tfrac{1}{2})}} / rank
 
Normal rank
Property / 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}}

m=1,2,\dots,\left\lfloor\tfrac{1}{2}n\right\rfloor
Property / 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}} / rank
 
Normal rank
Property / Symbols used
 
Property / Symbols used: the ratio of the circumference of a circle to its diameter / rank
 
Normal rank
Property / Symbols used: the ratio of the circumference of a circle to its diameter / qualifier
 
Defining formula:

π {\displaystyle{\displaystyle\pi}}

\cpi
Property / Symbols used: the ratio of the circumference of a circle to its diameter / qualifier
 
xml-id: C3.S12.E1.m2addec
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.m2acdec
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.m4aadec
Property / Symbols used
 
Property / Symbols used: Q10777 / rank
 
Normal rank
Property / Symbols used: Q10777 / qualifier
 
Defining formula:

( a , b ) 𝑎 𝑏 {\displaystyle{\displaystyle(\NVar{a},\NVar{b})}}

(\NVar{a},\NVar{b})
Property / Symbols used: Q10777 / qualifier
 
xml-id: introduction.Sx4.p1.t1.r29.m6adec
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.m1cdec
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.m1ddec
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.m1ddec

Latest revision as of 15:41, 2 January 2020

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DLMF:18.16.E5
No description defined

    Statements

    Defining formula
    θ n , m > ( m + 1 2 ⁢ α - 1 4 ) ⁢ π n + α + 1 2 , subscript 𝜃 𝑛 𝑚 𝑚 1 2 𝛼 1 4 𝜋 𝑛 𝛼 1 2 {\displaystyle{\displaystyle\theta_{n,m}>\frac{\left(m+\tfrac{1}{2}\alpha-% \tfrac{1}{4}\right){\pi}}{n+\alpha+\tfrac{1}{2}},}}
    0 references
    DLMF id
    DLMF:18.16.E5
    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 ∈ ( - 1 2 , 1 2 ) 𝛼 1 2 1 2 {\displaystyle{\displaystyle\alpha\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.m2addec
    0 references
    Q10784
    Defining formula
    ∈ {\displaystyle{\displaystyle\in}}
    xml-id
    introduction.Sx4.p1.t1.r10.m2acdec
    0 references
    Q11169
    Defining formula
    ⌊ x ⌋ 𝑥 {\displaystyle{\displaystyle\left\lfloor\NVar{x}\right\rfloor}}
    xml-id
    introduction.Sx4.p1.t1.r17.m4aadec
    0 references
    Q10777
    Defining formula
    ( a , b ) 𝑎 𝑏 {\displaystyle{\displaystyle(\NVar{a},\NVar{b})}}
    xml-id
    introduction.Sx4.p1.t1.r29.m6adec
    0 references
    Q11730
    Defining formula
    m 𝑚 {\displaystyle{\displaystyle m}}
    xml-id
    C18.S1.XMD5.m1cdec
    0 references
    Q11726
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C18.S1.XMD6.m1ddec
    0 references
    Q11760
    Defining formula
    θ n , m subscript 𝜃 𝑛 𝑚 {\displaystyle{\displaystyle\theta_{n,m}}}
    xml-id
    C18.S16.XMD1.m1ddec
    0 references
     
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