DLMF:1.15.E27 (Q569)

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DLMF:1.15.E27
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    Statements

    Defining formula
    G ⁢ ( z ) = G ⁢ ( x + i ⁢ y ) = u ⁢ ( x , y ) + i ⁢ v ⁢ ( x , y ) = F ⁢ ( 0 ) + 2 ⁢ ∑ n = 1 ∞ F ⁢ ( n ) ⁢ z n . 𝐺 𝑧 𝐺 𝑥 𝑖 𝑦 𝑢 𝑥 𝑦 𝑖 𝑣 𝑥 𝑦 𝐹 0 2 subscript superscript 𝑛 1 𝐹 𝑛 superscript 𝑧 𝑛 {\displaystyle{\displaystyle G(z)=G(x+iy)=u(x,y)+iv(x,y)=F(0)+2\sum^{\infty}_{% n=1}F(n)z^{n}.}}
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    DLMF id
    DLMF:1.15.E27
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    comment
    Warning: Falling back to standard tex;
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    Symbols used
    imaginary unit
    Defining formula
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    xml-id
    C1.S9.E1.m2afdec
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    Q10777
    Defining formula
    ( a , b ) 𝑎 𝑏 {\displaystyle{\displaystyle(\NVar{a},\NVar{b})}}
    xml-id
    introduction.Sx4.p1.t1.r29.m6adec
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    Q10760
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C1.S1.XMD1.m1dec
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    Q10757
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C1.S1.XMD7.m1vdec
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    DLMF:1.15.E19
    Defining formula
    F ⁢ ( n ) 𝐹 𝑛 {\displaystyle{\displaystyle F(n)}}
    xml-id
    C1.S15.XMD4.m1edec
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    Q10898
    Defining formula
    u ⁢ ( x , y ) 𝑢 𝑥 𝑦 {\displaystyle{\displaystyle u(x,y)}}
    xml-id
    C1.S15.XMD6.m1dec
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