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Formula:8995

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Digital Library of Mathematical Functions ID 28.12.E5

∫ 0 π me ν ⁡ ( x , q ) ⁢ me ν ⁡ ( - x , q ) ⁢ d x = π . superscript subscript 0 𝜋 Mathieu-me 𝜈 𝑥 𝑞 Mathieu-me 𝜈 𝑥 𝑞 𝑥 𝜋 {\displaystyle{\displaystyle\int_{0}^{\pi}\mathrm{me}_{\nu}\left(x,q\right)% \mathrm{me}_{\nu}\left(-x,q\right)\mathrm{d}x=\pi.}}


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
  • x 𝑥 {\displaystyle{\displaystyle x}} : real variable
  • ν 𝜈 {\displaystyle{\displaystyle\nu}} : complex parameter
  •  Edit this on Wikidata

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