DLMF:30.8.E8 (Q8874): Difference between revisions

From DRMF
Jump to navigation Jump to search
← Older editNewer edit →
‎Changed an Item: Add constraint
‎Changed an Item: Add constraint
Property / Symbols used
 
Property / Symbols used: Q12425 / rank
 
Normal rank
Property / Symbols used: Q12425 / qualifier
 
Defining formula:

A k subscript 𝐴 𝑘 {\displaystyle{\displaystyle A_{k}}}

A_{k}
Property / Symbols used: Q12425 / qualifier
 
xml-id: C30.S8.XMD3.m1bdec

Revision as of 01:46, 2 January 2020

No description defined
Language Label Description Also known as
English
DLMF:30.8.E8
No description defined

    Statements

    Defining formula
    λ n m ⁡ ( γ 2 ) - B k A k ⁢ a n , k m ⁢ ( γ 2 ) a n , k - 1 m ⁢ ( γ 2 ) = 1 + O ⁡ ( 1 k 4 ) . spheroidal-eigenvalue-lambda 𝑚 𝑛 superscript 𝛾 2 subscript 𝐵 𝑘 subscript 𝐴 𝑘 subscript superscript 𝑎 𝑚 𝑛 𝑘 superscript 𝛾 2 subscript superscript 𝑎 𝑚 𝑛 𝑘 1 superscript 𝛾 2 1 Big-O 1 superscript 𝑘 4 {\displaystyle{\displaystyle\frac{\lambda^{m}_{n}\left(\gamma^{2}\right)-B_{k}% }{A_{k}}\frac{a^{m}_{n,k}(\gamma^{2})}{a^{m}_{n,k-1}(\gamma^{2})}=1+O\left(% \frac{1}{k^{4}}\right).}}
    0 references
    DLMF id
    DLMF:30.8.E8
    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.m2aadec
    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.m1gdec
    0 references
    Q12409
    Defining formula
    n ≥ m 𝑛 𝑚 {\displaystyle{\displaystyle n\geq m}}
    xml-id
    C30.S1.XMD5.m1gdec
    0 references
    Q12404
    Defining formula
    γ 2 superscript 𝛾 2 {\displaystyle{\displaystyle\gamma^{2}}}
    xml-id
    C30.S2.XMD3.m1gdec
    0 references
    coefficients (locally)
    Defining formula
    a n , k m ⁢ ( γ 2 ) subscript superscript 𝑎 𝑚 𝑛 𝑘 superscript 𝛾 2 {\displaystyle{\displaystyle a^{m}_{n,k}(\gamma^{2})}}
    xml-id
    C30.S8.XMD2.m1edec
    0 references
    Q12425
    Defining formula
    A k subscript 𝐴 𝑘 {\displaystyle{\displaystyle A_{k}}}
    xml-id
    C30.S8.XMD3.m1bdec
    0 references
     
        Retrieved from "https://drmf-beta.wmflabs.org/index.php?title=Item:Q8874&oldid=34529"