DLMF:18.15.E7 (Q5697): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: order not exceeding / rank
 
Normal rank
Property / Symbols used: order not exceeding / qualifier
 
Defining formula:

O ⁡ ( x ) Big-O 𝑥 {\displaystyle{\displaystyle O\left(\NVar{x}\right)}}

\bigO@{\NVar{x}}
Property / Symbols used: order not exceeding / qualifier
 
xml-id: C2.S1.E3.m2aadec
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.m2abdec
Property / Symbols used
 
Property / Symbols used: Q11754 / rank
 
Normal rank
Property / Symbols used: Q11754 / qualifier
 
Defining formula:

δ 𝛿 {\displaystyle{\displaystyle\delta}}

\delta
Property / Symbols used: Q11754 / qualifier
 
xml-id: C18.S1.XMD8.m1dec
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

Latest revision as of 15:37, 2 January 2020

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DLMF:18.15.E7
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    Statements

    Defining formula
    ε M ⁢ ( ρ , θ ) = { θ ⁢ O ⁡ ( ρ - 2 ⁢ M - ( 3 / 2 ) ) , c ⁢ ρ - 1 ≤ θ ≤ π - δ , θ α + ( 5 / 2 ) ⁢ O ⁡ ( ρ - 2 ⁢ M + α ) , 0 ≤ θ ≤ c ⁢ ρ - 1 , subscript 𝜀 𝑀 𝜌 𝜃 cases 𝜃 Big-O superscript 𝜌 2 𝑀 3 2 𝑐 superscript 𝜌 1 𝜃 𝜋 𝛿 superscript 𝜃 𝛼 5 2 Big-O superscript 𝜌 2 𝑀 𝛼 0 𝜃 𝑐 superscript 𝜌 1 {\displaystyle{\displaystyle\varepsilon_{M}(\rho,\theta)=\begin{cases}\theta O% \left(\rho^{-2M-(3/2)}\right),&c\rho^{-1}\leq\theta\leq\pi-\delta,\\ \theta^{\alpha+(5/2)}O\left(\rho^{-2M+\alpha}\right),&0\leq\theta\leq c\rho^{-% 1},\end{cases}}}
    0 references
    DLMF id
    DLMF:18.15.E7
    0 references
    Symbols used
    order not exceeding
    Defining formula
    O ⁡ ( x ) Big-O 𝑥 {\displaystyle{\displaystyle O\left(\NVar{x}\right)}}
    xml-id
    C2.S1.E3.m2aadec
    0 references
    the ratio of the circumference of a circle to its diameter
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2abdec
    0 references
    Q11754
    Defining formula
    δ 𝛿 {\displaystyle{\displaystyle\delta}}
    xml-id
    C18.S1.XMD8.m1dec
    0 references
    DLMF:18.15.E5
    Defining formula
    ρ 𝜌 {\displaystyle{\displaystyle\rho}}
    xml-id
    C18.S15.XMD4.m1bdec
    0 references
     
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