DLMF:28.8.E7 (Q8272): Difference between revisions

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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.m1fdec

Latest revision as of 14:48, 2 January 2020

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DLMF:28.8.E7
No description defined

    Statements

    Defining formula
    S ^ m ∼ ( π ⁢ h 2 ⁢ ( m ! ) 2 ) 1 / 4 ⁢ ( 1 - 2 ⁢ m + 1 8 ⁢ h + m 4 + 2 ⁢ m 3 - 121 ⁢ m 2 - 122 ⁢ m - 84 2048 ⁢ h 2 + ⋯ ) - 1 / 2 . asymptotic-expansion subscript ^ 𝑆 𝑚 superscript 𝜋 ℎ 2 superscript 𝑚 2 1 4 superscript 1 2 𝑚 1 8 ℎ superscript 𝑚 4 2 superscript 𝑚 3 121 superscript 𝑚 2 122 𝑚 84 2048 superscript ℎ 2 ⋯ 1 2 {\displaystyle{\displaystyle\widehat{S}_{m}\sim\left(\frac{\pi h}{2(m!)^{2}}% \right)^{\ifrac{1}{4}}\left(1-\frac{2m+1}{8h}+\dfrac{m^{4}+2m^{3}-121m^{2}-122% m-84}{2048h^{2}}+\cdots\right)^{-\ifrac{1}{2}}.}}
    0 references
    DLMF id
    DLMF:28.8.E7
    0 references
    Symbols used
    Q10931
    Defining formula
    ∼ asymptotic-expansion {\displaystyle{\displaystyle\sim}}
    xml-id
    C2.S1.SS3.p1.m11addec
    0 references
    the ratio of the circumference of a circle to its diameter
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2abdec
    0 references
    Q10755
    Defining formula
    ! {\displaystyle{\displaystyle!}}
    xml-id
    introduction.Sx4.p1.t1.r15.m5addec
    0 references
    Q12284
    Defining formula
    m 𝑚 {\displaystyle{\displaystyle m}}
    xml-id
    C28.S1.XMD1.m1fdec
    0 references
    Q12294
    Defining formula
    h ℎ {\displaystyle{\displaystyle h}}
    xml-id
    C28.S1.XMD11.m1fdec
    0 references
     
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