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Formula:538

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Digital Library of Mathematical Functions ID 1.15.E27

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}.}}


Constraint(s)

Symbols List

  • i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}} : imaginary unit
  • ( a , b ) 𝑎 𝑏 {\displaystyle{\displaystyle(\NVar{a},\NVar{b})}} :
  • z 𝑧 {\displaystyle{\displaystyle z}} : variable
  • n 𝑛 {\displaystyle{\displaystyle n}} : nonnegative integer
  • F ⁢ ( n ) 𝐹 𝑛 {\displaystyle{\displaystyle F(n)}} : 1.15.E19
  • u ⁢ ( x , y ) 𝑢 𝑥 𝑦 {\displaystyle{\displaystyle u(x,y)}} : function
  •  Edit this on Wikidata

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This page was last edited on 3 March 2024, at 02:32.
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