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Formula:9050

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Digital Library of Mathematical Functions ID 28.20.E22

M ν ( j ) ⁡ ( z ± 1 2 ⁢ π ⁢ i , h ) = M ν ( j ) ⁡ ( z , ± i ⁢ h ) , modified-Mathieu-M 𝑗 𝜈 plus-or-minus 𝑧 1 2 𝜋 imaginary-unit ℎ modified-Mathieu-M 𝑗 𝜈 𝑧 plus-or-minus imaginary-unit ℎ {\displaystyle{\displaystyle{\mathrm{M}^{(j)}_{\nu}}\left(z\pm\tfrac{1}{2}\pi% \mathrm{i},h\right)={\mathrm{M}^{(j)}_{\nu}}\left(z,\pm\mathrm{i}h\right),}}


Constraint(s)

ν ∉ ℤ 𝜈 {\displaystyle{\displaystyle\nu\notin\mathbb{Z}}}

Symbols List

  • π {\displaystyle{\displaystyle\pi}} : the ratio of the circumference of a circle to its diameter
  • i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}} : imaginary unit
  • ℤ {\displaystyle{\displaystyle\mathbb{Z}}} :
  • M ν ( j ) ⁡ ( z , h ) modified-Mathieu-M 𝑗 𝜈 𝑧 ℎ {\displaystyle{\displaystyle{\mathrm{M}^{(\NVar{j})}_{\NVar{\nu}}}\left(\NVar{% z},\NVar{h}\right)}} :
  • ∉ {\displaystyle{\displaystyle\notin}} :
  • h ℎ {\displaystyle{\displaystyle h}} : parameter
  • j 𝑗 {\displaystyle{\displaystyle j}} : integer
  • z 𝑧 {\displaystyle{\displaystyle z}} : complex variable
  • ν 𝜈 {\displaystyle{\displaystyle\nu}} : complex parameter
  •  Edit this on Wikidata

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