DLMF:1.9.E34 (Q309)

From DRMF
Jump to navigation Jump to search
No description defined
Language Label Description Also known as
English
DLMF:1.9.E34
No description defined

    Statements

    Defining formula
    u ⁢ ( r ⁢ e i ⁢ θ ) = 1 2 ⁢ π ⁢ ∫ 0 2 ⁢ π ( R 2 - r 2 ) ⁢ h ⁢ ( R ⁢ e i ⁢ ϕ ) ⁢ d ϕ R 2 - 2 ⁢ R ⁢ r ⁢ cos ⁡ ( ϕ - θ ) + r 2 𝑢 𝑟 superscript 𝑒 𝑖 𝜃 1 2 𝜋 subscript superscript 2 𝜋 0 superscript 𝑅 2 superscript 𝑟 2 ℎ 𝑅 superscript 𝑒 𝑖 italic-ϕ italic-ϕ superscript 𝑅 2 2 𝑅 𝑟 italic-ϕ 𝜃 superscript 𝑟 2 {\displaystyle{\displaystyle u(re^{i\theta})=\frac{1}{2\pi}\int^{2\pi}_{0}% \frac{(R^{2}-r^{2})h(Re^{i\phi})\mathrm{d}\phi}{R^{2}-2Rr\cos\left(\phi-\theta% \right)+r^{2}}}}
    0 references
    DLMF id
    DLMF:1.9.E34
    0 references
    Symbols used
    the ratio of the circumference of a circle to its diameter
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2agdec
    0 references
    cosine function
    Defining formula
    cos ⁡ z 𝑧 {\displaystyle{\displaystyle\cos\NVar{z}}}
    xml-id
    C4.S14.E2.m2acdec
    0 references
    Q10770
    Defining formula
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1afdec
    0 references
    base of natural logarithm
    Defining formula
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2acdec
    0 references
    imaginary unit
    Defining formula
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    xml-id
    C1.S9.E1.m2andec
    0 references
    Q10771
    Defining formula
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3afdec
    0 references
    Q10813
    Defining formula
    r 𝑟 {\displaystyle{\displaystyle r}}
    xml-id
    C1.S9.XMD1.m1fdec
    0 references
    Q10822
    Defining formula
    u ⁢ ( z ) 𝑢 𝑧 {\displaystyle{\displaystyle u(z)}}
    xml-id
    C1.S9.XMD14.m1adec
    0 references
    Q10823
    Defining formula
    R 𝑅 {\displaystyle{\displaystyle R}}
    xml-id
    C1.S9.XMD15.m1dec
    0 references
     
        Retrieved from "https://drmf-beta.wmflabs.org/index.php?title=Item:Q309&oldid=22827"