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Formula:6329

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Digital Library of Mathematical Functions ID 18.10.E8

p n ⁢ ( x ) = g 0 ⁢ ( x ) 2 ⁢ π ⁢ i ⁢ ∫ C ( g 1 ⁢ ( z , x ) ) n ⁢ g 2 ⁢ ( z , x ) ⁢ ( z - c ) - 1 ⁢ d z subscript 𝑝 𝑛 𝑥 subscript 𝑔 0 𝑥 2 𝜋 𝑖 subscript 𝐶 superscript subscript 𝑔 1 𝑧 𝑥 𝑛 subscript 𝑔 2 𝑧 𝑥 superscript 𝑧 𝑐 1 𝑧 {\displaystyle{\displaystyle p_{n}(x)=\frac{g_{0}(x)}{2\pi i}\int_{C}\left(g_{% 1}(z,x)\right)^{n}g_{2}(z,x)(z-c)^{-1}\mathrm{d}z}}


Constraint(s)

Symbols List

  • π {\displaystyle{\displaystyle\pi}} : the ratio of the circumference of a circle to its diameter
  • d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}} : differential of x
  • i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}} : imaginary unit
  • ∫ {\displaystyle{\displaystyle\int}} : integral
  • z 𝑧 {\displaystyle{\displaystyle z}} : complex variable
  • n 𝑛 {\displaystyle{\displaystyle n}} : nonnegative integer
  • p n ⁢ ( x ) subscript 𝑝 𝑛 𝑥 {\displaystyle{\displaystyle p_{n}(x)}} : polynomial of degree n
  • C 𝐶 {\displaystyle{\displaystyle C}} : closed contour
  • x 𝑥 {\displaystyle{\displaystyle x}} : real variable
  •  Edit this on Wikidata

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