DLMF:28.14.E10 (Q8324): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Q10755 / rank
 
Normal rank
Property / Symbols used: Q10755 / qualifier
 
Defining formula:

! {\displaystyle{\displaystyle!}}

!
Property / Symbols used: Q10755 / qualifier
 
xml-id: introduction.Sx4.p1.t1.r15.m5adec
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.m1idec
Property / Symbols used
 
Property / Symbols used: Q12271 / rank
 
Normal rank
Property / Symbols used: Q12271 / qualifier
 
Defining formula:

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

q=h^{2}
Property / Symbols used: Q12271 / qualifier
 
xml-id: C28.S1.XMD10.m1hdec
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.m1idec
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.m1idec

Latest revision as of 14:57, 2 January 2020

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DLMF:28.14.E10
No description defined

    Statements

    Defining formula
    c 2 ⁢ m ν ⁢ ( q ) = ( ( - 1 ) m ⁢ q m ⁢ Γ ⁡ ( ν + 1 ) m ! ⁢  2 2 ⁢ m ⁢ Γ ⁡ ( ν + m + 1 ) + O ⁡ ( q m + 2 ) ) ⁢ c 0 ν ⁢ ( q ) . superscript subscript 𝑐 2 𝑚 𝜈 𝑞 superscript 1 𝑚 superscript 𝑞 𝑚 Euler-Gamma 𝜈 1 𝑚 superscript  2 2 𝑚 Euler-Gamma 𝜈 𝑚 1 Big-O superscript 𝑞 𝑚 2 superscript subscript 𝑐 0 𝜈 𝑞 {\displaystyle{\displaystyle c_{2m}^{\nu}(q)=\left(\frac{(-1)^{m}q^{m}\Gamma% \left(\nu+1\right)}{m!\,2^{2m}\Gamma\left(\nu+m+1\right)}+O\left(q^{m+2}\right% )\right)c_{0}^{\nu}(q).}}
    0 references
    DLMF id
    DLMF:28.14.E10
    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
    gamma function
    Defining formula
    Γ ⁡ ( z ) Euler-Gamma 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
    xml-id
    C5.S2.E1.m2adec
    0 references
    Q10755
    Defining formula
    ! {\displaystyle{\displaystyle!}}
    xml-id
    introduction.Sx4.p1.t1.r15.m5adec
    0 references
    Q12284
    Defining formula
    m 𝑚 {\displaystyle{\displaystyle m}}
    xml-id
    C28.S1.XMD1.m1idec
    0 references
    Q12271
    Defining formula
    q = h 2 𝑞 superscript ℎ 2 {\displaystyle{\displaystyle q=h^{2}}}
    xml-id
    C28.S1.XMD10.m1hdec
    0 references
    Q12278
    Defining formula
    ν 𝜈 {\displaystyle{\displaystyle\nu}}
    xml-id
    C28.S1.XMD7.m1idec
    0 references
    Q12300
    Defining formula
    c 2 ⁢ m ⁢ ( q ) subscript 𝑐 2 𝑚 𝑞 {\displaystyle{\displaystyle c_{2m}(q)}}
    xml-id
    C28.S14.XMD1.m1idec
    0 references
     
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