DLMF:28.8.E5 (Q8270): Difference between revisions

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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.m1ddec
Property / Symbols used
 
Property / Symbols used: Q12294 / rank
 
Normal rank
Property / Symbols used: Q12294 / qualifier
 
Defining formula:

h ℎ {\displaystyle{\displaystyle h}}

h
Property / Symbols used: Q12294 / qualifier
 
xml-id: C28.S1.XMD11.m1ddec
Property / Symbols used
 
Property / Symbols used: Q12295 / rank
 
Normal rank
Property / Symbols used: Q12295 / qualifier
 
Defining formula:

ξ 𝜉 {\displaystyle{\displaystyle\xi}}

\xi
Property / Symbols used: Q12295 / qualifier
 
xml-id: C28.S8.XMD1.m1bdec

Latest revision as of 14:48, 2 January 2020

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DLMF:28.8.E5
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    Statements

    Defining formula
    V m ⁢ ( ξ ) ∼ 1 2 4 ⁢ h ⁢ ( - D m + 2 ⁡ ( ξ ) - m ⁢ ( m - 1 ) ⁢ D m - 2 ⁡ ( ξ ) ) + 1 2 10 ⁢ h 2 ⁢ ( D m + 6 ⁡ ( ξ ) + ( m 2 - 25 ⁢ m - 36 ) ⁢ D m + 2 ⁡ ( ξ ) - m ⁢ ( m - 1 ) ⁢ ( m 2 + 27 ⁢ m - 10 ) ⁢ D m - 2 ⁡ ( ξ ) - 6 ! ⁢ ( m 6 ) ⁢ D m - 6 ⁡ ( ξ ) ) + ⋯ , asymptotic-expansion subscript 𝑉 𝑚 𝜉 1 superscript 2 4 ℎ Whittaker-D 𝑚 2 𝜉 𝑚 𝑚 1 Whittaker-D 𝑚 2 𝜉 1 superscript 2 10 superscript ℎ 2 Whittaker-D 𝑚 6 𝜉 superscript 𝑚 2 25 𝑚 36 Whittaker-D 𝑚 2 𝜉 𝑚 𝑚 1 superscript 𝑚 2 27 𝑚 10 Whittaker-D 𝑚 2 𝜉 6 binomial 𝑚 6 Whittaker-D 𝑚 6 𝜉 ⋯ {\displaystyle{\displaystyle V_{m}(\xi)\sim\frac{1}{2^{4}h}\bigg{(}-D_{m+2}% \left(\xi\right)-m(m-1)D_{m-2}\left(\xi\right)\bigg{)}+\frac{1}{2^{10}h^{2}}% \left(D_{m+6}\left(\xi\right)+(m^{2}-25m-36)D_{m+2}\left(\xi\right)-m(m-1)(m^{% 2}+27m-10)D_{m-2}\left(\xi\right)-6!\genfrac{(}{)}{0.0pt}{}{m}{6}D_{m-6}\left(% \xi\right)\right)+\cdots,}}
    0 references
    DLMF id
    DLMF:28.8.E5
    0 references
    Symbols used
    Q11515
    Defining formula
    D ν ⁡ ( z ) Whittaker-D 𝜈 𝑧 {\displaystyle{\displaystyle D_{\NVar{\nu}}\left(\NVar{z}\right)}}
    xml-id
    C12.S1.p3.m6aadec
    0 references
    Q10931
    Defining formula
    ∼ asymptotic-expansion {\displaystyle{\displaystyle\sim}}
    xml-id
    C2.S1.SS3.p1.m11abdec
    0 references
    Q10754
    Defining formula
    ( m n ) binomial 𝑚 𝑛 {\displaystyle{\displaystyle\genfrac{(}{)}{0.0pt}{}{\NVar{m}}{\NVar{n}}}}
    xml-id
    C1.S2.SS1.m1aadec
    0 references
    Q10755
    Defining formula
    ! {\displaystyle{\displaystyle!}}
    xml-id
    introduction.Sx4.p1.t1.r15.m5abdec
    0 references
    Q12284
    Defining formula
    m 𝑚 {\displaystyle{\displaystyle m}}
    xml-id
    C28.S1.XMD1.m1ddec
    0 references
    Q12294
    Defining formula
    h ℎ {\displaystyle{\displaystyle h}}
    xml-id
    C28.S1.XMD11.m1ddec
    0 references
    Q12295
    Defining formula
    ξ 𝜉 {\displaystyle{\displaystyle\xi}}
    xml-id
    C28.S8.XMD1.m1bdec
    0 references
     
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