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Formula:9007

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Digital Library of Mathematical Functions ID 28.14.E1

me ν ⁡ ( z , q ) = ∑ m = - ∞ ∞ c 2 ⁢ m ν ⁢ ( q ) ⁢ e i ⁢ ( ν + 2 ⁢ m ) ⁢ z , Mathieu-me 𝜈 𝑧 𝑞 superscript subscript 𝑚 subscript superscript 𝑐 𝜈 2 𝑚 𝑞 superscript 𝑒 imaginary-unit 𝜈 2 𝑚 𝑧 {\displaystyle{\displaystyle\mathrm{me}_{\nu}\left(z,q\right)=\sum_{m=-\infty}% ^{\infty}c^{\nu}_{2m}(q)e^{\mathrm{i}(\nu+2m)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)}} :
  • e {\displaystyle{\displaystyle\mathrm{e}}} : base of natural logarithm
  • i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}} : imaginary unit
  • m 𝑚 {\displaystyle{\displaystyle m}} : integer
  • q = h 2 𝑞 superscript ℎ 2 {\displaystyle{\displaystyle q=h^{2}}} : parameter
  • z 𝑧 {\displaystyle{\displaystyle z}} : complex variable
  • ν 𝜈 {\displaystyle{\displaystyle\nu}} : complex parameter
  • c 2 ⁢ m ⁢ ( q ) subscript 𝑐 2 𝑚 𝑞 {\displaystyle{\displaystyle c_{2m}(q)}} : coefficients
  •  Edit this on Wikidata

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This page was last edited on 28 January 2024, at 10:30.
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