DLMF:10.20.E2 (Q3251)

From DRMF
Jump to navigation Jump to search
No description defined
Language Label Description Also known as
English
DLMF:10.20.E2
No description defined

    Statements

    Defining formula
    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
    Defining formula
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1adec
    0 references
    Q10771
    Defining formula
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3adec
    0 references
    principal branch of logarithm function
    Defining formula
    ln ⁡ z 𝑧 {\displaystyle{\displaystyle\ln\NVar{z}}}
    xml-id
    C4.S2.E2.m2adec
    0 references
    Q11426
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C10.S1.XMD6.m1adec
    0 references
    Q11451
    Defining formula
    ζ ⁢ ( z ) 𝜁 𝑧 {\displaystyle{\displaystyle\zeta(z)}}
    xml-id
    C10.S20.XMD1.m1adec
    0 references
     
        Retrieved from "https://drmf-beta.wmflabs.org/index.php?title=Item:Q3251&oldid=59404"