DLMF:10.20.E2 (Q3251): Difference between revisions

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Property / constraint
 

0 < z ≤ 1 0 𝑧 1 {\displaystyle{\displaystyle 0<z\leq 1}}

0<z\leq 1
Property / constraint: 0 < z ≤ 1 0 𝑧 1 {\displaystyle{\displaystyle 0<z\leq 1}} / rank
 
Normal rank
Property / Symbols used
 
Property / Symbols used: Q10770 / rank
 
Normal rank
Property / Symbols used: Q10770 / qualifier
 
test:

d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}

\diff{\NVar{x}}
Property / Symbols used: Q10770 / qualifier
 
xml-id: C1.S4.SS4.m1adec
Property / Symbols used
 
Property / Symbols used: Q10771 / rank
 
Normal rank
Property / Symbols used: Q10771 / qualifier
 
test:

∫ {\displaystyle{\displaystyle\int}}

\int
Property / Symbols used: Q10771 / qualifier
 
xml-id: C1.S4.SS4.m3adec
Property / Symbols used
 
Property / Symbols used: principal branch of logarithm function / rank
 
Normal rank
Property / Symbols used: principal branch of logarithm function / qualifier
 
test:

ln ⁡ z 𝑧 {\displaystyle{\displaystyle\ln\NVar{z}}}

\ln@@{\NVar{z}}
Property / Symbols used: principal branch of logarithm function / qualifier
 
xml-id: C4.S2.E2.m2adec
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.m1adec
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.m1adec

Latest revision as of 14:37, 2 January 2020

No description defined
Language Label Description Also known as
English
DLMF:10.20.E2
No description defined

    Statements

    test
    2 3 ⁢ ζ 3 2 = ∫ z 1 1 - t 2 t ⁢ d t = ln ⁡ ( 1 + 1 - z 2 z ) - 1 - z 2 , 2 3 superscript 𝜁 3 2 superscript subscript 𝑧 1 1 superscript 𝑡 2 𝑡 𝑡 1 1 superscript 𝑧 2 𝑧 1 superscript 𝑧 2 {\displaystyle{\displaystyle\frac{2}{3}\zeta^{\frac{3}{2}}=\int_{z}^{1}\frac{% \sqrt{1-t^{2}}}{t}\mathrm{d}t=\ln\left(\frac{1+\sqrt{1-z^{2}}}{z}\right)-\sqrt% {1-z^{2}},}}
    0 references
    DLMF id
    DLMF:10.20.E2
    0 references
    constraint
    0 < z ≤ 1 0 𝑧 1 {\displaystyle{\displaystyle 0<z\leq 1}}
    0 references
    Symbols used
    Q10770
    test
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1adec
    0 references
    Q10771
    test
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3adec
    0 references
    principal branch of logarithm function
    test
    ln ⁡ z 𝑧 {\displaystyle{\displaystyle\ln\NVar{z}}}
    xml-id
    C4.S2.E2.m2adec
    0 references
    Q11426
    test
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C10.S1.XMD6.m1adec
    0 references
    Q11451
    test
    ζ ⁢ ( z ) 𝜁 𝑧 {\displaystyle{\displaystyle\zeta(z)}}
    xml-id
    C10.S20.XMD1.m1adec
    0 references
     
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