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Formula:9517

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Digital Library of Mathematical Functions ID 30.3.E2

λ n m ⁡ ( γ 2 ) = n ⁢ ( n + 1 ) - 1 2 ⁢ γ 2 + O ⁡ ( n - 2 ) , spheroidal-eigenvalue-lambda 𝑚 𝑛 superscript 𝛾 2 𝑛 𝑛 1 1 2 superscript 𝛾 2 Big-O superscript 𝑛 2 {\displaystyle{\displaystyle\lambda^{m}_{n}\left(\gamma^{2}\right)=n(n+1)-% \tfrac{1}{2}\gamma^{2}+O\left(n^{-2}\right),}}


Constraint(s)

n → ∞ → 𝑛 {\displaystyle{\displaystyle n\to\infty}}

Symbols List

  • O ⁡ ( x ) Big-O 𝑥 {\displaystyle{\displaystyle O\left(\NVar{x}\right)}} : order not exceeding
  • λ n m ⁡ ( γ 2 ) spheroidal-eigenvalue-lambda 𝑚 𝑛 superscript 𝛾 2 {\displaystyle{\displaystyle\lambda^{\NVar{m}}_{\NVar{n}}\left(\NVar{\gamma^{2% }}\right)}} :
  • m 𝑚 {\displaystyle{\displaystyle m}} : nonnegative integer
  • n ≥ m 𝑛 𝑚 {\displaystyle{\displaystyle n\geq m}} : integer degree
  • γ 2 superscript 𝛾 2 {\displaystyle{\displaystyle\gamma^{2}}} : real parameter
  •  Edit this on Wikidata

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This page was last edited on 28 January 2024, at 10:02.
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