DLMF:10.20.E3 (Q3252): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Q11426 / rank
 
Normal rank
Property / Symbols used: Q11426 / qualifier
 
test:

z 𝑧 {\displaystyle{\displaystyle z}}

z
Property / Symbols used: Q11426 / qualifier
 
xml-id: C10.S1.XMD6.m1bdec
Property / Symbols used
 
Property / Symbols used: Q11451 / rank
 
Normal rank
Property / Symbols used: Q11451 / qualifier
 
test:

ζ ⁢ ( z ) 𝜁 𝑧 {\displaystyle{\displaystyle\zeta(z)}}

\zeta(z)
Property / Symbols used: Q11451 / qualifier
 
xml-id: C10.S20.XMD1.m1bdec

Latest revision as of 15:37, 2 January 2020

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DLMF:10.20.E3
No description defined

    Statements

    test
    2 3 ⁢ ( - ζ ) 3 2 = ∫ 1 z t 2 - 1 t ⁢ d t = z 2 - 1 - arcsec ⁡ z , 2 3 superscript 𝜁 3 2 superscript subscript 1 𝑧 superscript 𝑡 2 1 𝑡 𝑡 superscript 𝑧 2 1 𝑧 {\displaystyle{\displaystyle\frac{2}{3}(-\zeta)^{\frac{3}{2}}=\int_{1}^{z}% \frac{\sqrt{t^{2}-1}}{t}\mathrm{d}t=\sqrt{z^{2}-1}-\operatorname{arcsec}z,}}
    0 references
    DLMF id
    DLMF:10.20.E3
    0 references
    constraint
    1 ≤ z < ∞ 1 𝑧 {\displaystyle{\displaystyle 1\leq z<\infty}}
    0 references
    Symbols used
    Q10770
    test
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1aadec
    0 references
    Q10771
    test
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3aadec
    0 references
    arcsecant function
    test
    arcsec ⁡ z 𝑧 {\displaystyle{\displaystyle\operatorname{arcsec}\NVar{z}}}
    xml-id
    C4.S23.E8.m2adec
    0 references
    Q11426
    test
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C10.S1.XMD6.m1bdec
    0 references
    Q11451
    test
    ζ ⁢ ( z ) 𝜁 𝑧 {\displaystyle{\displaystyle\zeta(z)}}
    xml-id
    C10.S20.XMD1.m1bdec
    0 references
     
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