DLMF:5.11.E11 (Q2133): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Q11273 / rank
 
Normal rank
Property / Symbols used: Q11273 / qualifier
 
Defining formula:

z 𝑧 {\displaystyle{\displaystyle z}}

z
Property / Symbols used: Q11273 / qualifier
 
xml-id: C5.S1.XMD7.m1fdec

Latest revision as of 19:41, 1 January 2020

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DLMF:5.11.E11
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    Statements

    Defining formula
    | R K ⁢ ( z ) | ≤ ( 1 + ζ ⁡ ( K ) ) ⁢ Γ ⁡ ( K ) 2 ⁢ ( 2 ⁢ π ) K + 1 ⁢ | z | K ⁢ ( 1 + min ⁡ ( sec ⁡ ( ph ⁡ z ) , 2 ⁢ K 1 2 ) ) , subscript 𝑅 𝐾 𝑧 1 Riemann-zeta 𝐾 Euler-Gamma 𝐾 2 superscript 2 𝜋 𝐾 1 𝑧 𝐾 1 phase 𝑧 2 superscript 𝐾 1 2 {\displaystyle{\displaystyle\left|R_{K}(z)\right|\leq\frac{(1+\zeta\left(K% \right))\Gamma\left(K\right)}{2(2\pi)^{K+1}{\left|z\right|^{K}}}\*\left(1+\min% (\sec\left(\operatorname{ph}z\right),2K^{\frac{1}{2}})\right),}}
    0 references
    DLMF id
    DLMF:5.11.E11
    0 references
    constraint
    | ph ⁡ z | ≤ 1 2 ⁢ π phase 𝑧 1 2 𝜋 {\displaystyle{\displaystyle\left|\operatorname{ph}z\right|\leq\frac{1}{2}\pi}}
    0 references
    Symbols used
    gamma function
    Defining formula
    Γ ⁡ ( z ) Euler-Gamma 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
    xml-id
    C5.S2.E1.m2afdec
    0 references
    Riemann zeta function
    Defining formula
    ζ ⁡ ( s ) Riemann-zeta 𝑠 {\displaystyle{\displaystyle\zeta\left(\NVar{s}\right)}}
    xml-id
    C25.S2.E1.m2adec
    0 references
    the ratio of the circumference of a circle to its diameter
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2afdec
    0 references
    Q10817
    Defining formula
    ph phase {\displaystyle{\displaystyle\operatorname{ph}}}
    xml-id
    C1.S9.E7.m1adec
    0 references
    secant function
    Defining formula
    sec ⁡ z 𝑧 {\displaystyle{\displaystyle\sec\NVar{z}}}
    xml-id
    C4.S14.E6.m2adec
    0 references
    Q11273
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C5.S1.XMD7.m1fdec
    0 references
     
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