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Formula:9024

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Digital Library of Mathematical Functions ID 28.19.E3

f n = 1 π ⁢ ∫ 0 π f ⁢ ( z ) ⁢ me ν + 2 ⁢ n ⁡ ( - z , q ) ⁢ d z . subscript 𝑓 𝑛 1 𝜋 superscript subscript 0 𝜋 𝑓 𝑧 Mathieu-me 𝜈 2 𝑛 𝑧 𝑞 𝑧 {\displaystyle{\displaystyle f_{n}=\frac{1}{\pi}\int_{0}^{\pi}f(z)\mathrm{me}_% {\nu+2n}\left(-z,q\right)\mathrm{d}z.}}


Constraint(s)

Symbols List

  • me n ⁡ ( z , q ) Mathieu-me 𝑛 𝑧 𝑞 {\displaystyle{\displaystyle\mathrm{me}_{\NVar{n}}\left(\NVar{z},\NVar{q}% \right)}} :
  • 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
  • ∫ {\displaystyle{\displaystyle\int}} : integral
  • q = h 2 𝑞 superscript ℎ 2 {\displaystyle{\displaystyle q=h^{2}}} : parameter
  • n 𝑛 {\displaystyle{\displaystyle n}} : integer
  • z 𝑧 {\displaystyle{\displaystyle z}} : complex variable
  • ν 𝜈 {\displaystyle{\displaystyle\nu}} : complex parameter
  • f ⁢ ( z ) 𝑓 𝑧 {\displaystyle{\displaystyle f(z)}} : function (locally)
  •  Edit this on Wikidata

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