DLMF:28.14.E6 (Q8319): Difference between revisions

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Changed an Item: Add constraint
Changed an Item: Add constraint
 
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Property / Symbols used
 
Property / Symbols used: order not exceeding / rank
 
Normal rank
Property / Symbols used: order not exceeding / qualifier
 
Defining formula:

O ( x ) Big-O 𝑥 {\displaystyle{\displaystyle O\left(\NVar{x}\right)}}

\bigO@{\NVar{x}}
Property / Symbols used: order not exceeding / qualifier
 
xml-id: C2.S1.E3.m2adec
Property / Symbols used
 
Property / Symbols used: Q12284 / rank
 
Normal rank
Property / Symbols used: Q12284 / qualifier
 
Defining formula:

m 𝑚 {\displaystyle{\displaystyle m}}

m
Property / Symbols used: Q12284 / qualifier
 
xml-id: C28.S1.XMD1.m1edec
Property / Symbols used
 
Property / Symbols used: Q12271 / rank
 
Normal rank
Property / Symbols used: Q12271 / qualifier
 
Defining formula:

q = h 2 𝑞 superscript 2 {\displaystyle{\displaystyle q=h^{2}}}

q=h^{2}
Property / Symbols used: Q12271 / qualifier
 
xml-id: C28.S1.XMD10.m1edec
Property / Symbols used
 
Property / Symbols used: Q12278 / rank
 
Normal rank
Property / Symbols used: Q12278 / qualifier
 
Defining formula:

ν 𝜈 {\displaystyle{\displaystyle\nu}}

\nu
Property / Symbols used: Q12278 / qualifier
 
xml-id: C28.S1.XMD7.m1edec
Property / Symbols used
 
Property / Symbols used: Q12300 / rank
 
Normal rank
Property / Symbols used: Q12300 / qualifier
 
Defining formula:

c 2 m ( q ) subscript 𝑐 2 𝑚 𝑞 {\displaystyle{\displaystyle c_{2m}(q)}}

c_{2m}(q)
Property / Symbols used: Q12300 / qualifier
 
xml-id: C28.S14.XMD1.m1edec

Latest revision as of 14:57, 2 January 2020

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DLMF:28.14.E6
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    Statements

    c 2 m ν ( q ) c 2 m 2 ν ( q ) = - q 4 m 2 ( 1 + O ( 1 m ) ) , subscript superscript 𝑐 𝜈 2 𝑚 𝑞 subscript superscript 𝑐 𝜈 minus-or-plus 2 𝑚 2 𝑞 𝑞 4 superscript 𝑚 2 1 Big-O 1 𝑚 {\displaystyle{\displaystyle\frac{c^{\nu}_{2m}(q)}{c^{\nu}_{2m\mp 2}(q)}=\frac% {-q}{4m^{2}}\left(1+O\left(\frac{1}{m}\right)\right),}}
    0 references
    DLMF:28.14.E6
    0 references
    m ± 𝑚 plus-or-minus {\displaystyle{\displaystyle m\to\pm\infty}}
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    O ( x ) Big-O 𝑥 {\displaystyle{\displaystyle O\left(\NVar{x}\right)}}
    C2.S1.E3.m2adec
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    m 𝑚 {\displaystyle{\displaystyle m}}
    C28.S1.XMD1.m1edec
    0 references
    q = h 2 𝑞 superscript 2 {\displaystyle{\displaystyle q=h^{2}}}
    C28.S1.XMD10.m1edec
    0 references
    ν 𝜈 {\displaystyle{\displaystyle\nu}}
    C28.S1.XMD7.m1edec
    0 references
    c 2 m ( q ) subscript 𝑐 2 𝑚 𝑞 {\displaystyle{\displaystyle c_{2m}(q)}}
    C28.S14.XMD1.m1edec
    0 references