DLMF:30.3.E2 (Q8825): Difference between revisions

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‎Changed an Item: Add constraint
‎Changed an Item: Add constraint
Property / Symbols used
 
Property / Symbols used: Q12409 / rank
 
Normal rank
Property / Symbols used: Q12409 / qualifier
 
Defining formula:

n ≥ m 𝑛 𝑚 {\displaystyle{\displaystyle n\geq m}}

n\geq m
Property / Symbols used: Q12409 / qualifier
 
xml-id: C30.S1.XMD5.m1dec

Revision as of 01:40, 2 January 2020

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DLMF:30.3.E2
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    Statements

    Defining formula
    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),}}
    0 references
    DLMF id
    DLMF:30.3.E2
    0 references
    constraint
    n → ∞ → 𝑛 {\displaystyle{\displaystyle n\to\infty}}
    0 references
    Symbols used
    order not exceeding
    Defining formula
    O ⁡ ( x ) Big-O 𝑥 {\displaystyle{\displaystyle O\left(\NVar{x}\right)}}
    xml-id
    C2.S1.E3.m2adec
    0 references
    Q12407
    Defining formula
    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)}}
    xml-id
    C30.S3.SS1.p1.m2aadec
    0 references
    Q12408
    Defining formula
    m 𝑚 {\displaystyle{\displaystyle m}}
    xml-id
    C30.S1.XMD4.m1adec
    0 references
    Q12409
    Defining formula
    n ≥ m 𝑛 𝑚 {\displaystyle{\displaystyle n\geq m}}
    xml-id
    C30.S1.XMD5.m1dec
    0 references
     
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