DLMF:30.16.E4 (Q8964)

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DLMF:30.16.E4
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    Statements

    Defining formula
    α p , d - λ n m ⁡ ( γ 2 ) = O ⁡ ( γ 4 ⁢ d 4 2 ⁢ d + 1 ⁢ ( ( m + 2 ⁢ d - 1 ) ! ⁢ ( m + 2 ⁢ d + 1 ) ! ) 2 ) , subscript 𝛼 𝑝 𝑑 spheroidal-eigenvalue-lambda 𝑚 𝑛 superscript 𝛾 2 Big-O superscript 𝛾 4 𝑑 superscript 4 2 𝑑 1 superscript 𝑚 2 𝑑 1 𝑚 2 𝑑 1 2 {\displaystyle{\displaystyle\alpha_{p,d}-\lambda^{m}_{n}\left(\gamma^{2}\right% )=O\left(\frac{\gamma^{4d}}{4^{2d+1}((m+2d-1)!(m+2d+1)!)^{2}}\right),}}
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    DLMF id
    DLMF:30.16.E4
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    constraint
    d → ∞ → 𝑑 {\displaystyle{\displaystyle d\to\infty}}
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