DLMF:11.6.E4 (Q3980): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Q10931 / rank
 
Normal rank
Property / Symbols used: Q10931 / qualifier
 
test:

∼ asymptotic-expansion {\displaystyle{\displaystyle\sim}}

\asympexp
Property / Symbols used: Q10931 / qualifier
 
xml-id: C2.S1.SS3.p1.m11acdec

Revision as of 13:46, 2 January 2020

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DLMF:11.6.E4
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    Statements

    test
    ∫ 0 z 𝐌 0 ⁡ ( t ) ⁢ d t + 2 π ⁢ ( ln ⁡ ( 2 ⁢ z ) + γ ) ∼ 2 π ⁢ ∑ k = 1 ∞ ( 2 ⁢ k ) ! ⁢ ( 2 ⁢ k - 1 ) ! ( k ! ) 2 ⁢ ( 2 ⁢ z ) 2 ⁢ k , asymptotic-expansion superscript subscript 0 𝑧 associated-Struve-M 0 𝑡 𝑡 2 𝜋 2 𝑧 2 𝜋 superscript subscript 𝑘 1 2 𝑘 2 𝑘 1 superscript 𝑘 2 superscript 2 𝑧 2 𝑘 {\displaystyle{\displaystyle\int_{0}^{z}\mathbf{M}_{0}\left(t\right)\mathrm{d}% t+\frac{2}{\pi}(\ln\left(2z\right)+\gamma)\sim\frac{2}{\pi}\sum_{k=1}^{\infty}% \frac{(2k)!(2k-1)!}{(k!)^{2}(2z)^{2k}},}}
    0 references
    DLMF id
    DLMF:11.6.E4
    0 references
    constraint
    | ph ⁡ z | ≤ 1 2 ⁢ π - δ phase 𝑧 1 2 𝜋 𝛿 {\displaystyle{\displaystyle|\operatorname{ph}z|\leq\tfrac{1}{2}\pi-\delta}}
    0 references
    Symbols used
    Euler’s constant
    test
    γ {\displaystyle{\displaystyle\gamma}}
    xml-id
    C5.S2.E3.m2aadec
    0 references
    modified Struve function
    test
    𝐌 ν ⁡ ( z ) associated-Struve-M 𝜈 𝑧 {\displaystyle{\displaystyle\mathbf{M}_{\NVar{\nu}}\left(\NVar{z}\right)}}
    xml-id
    C11.S2.E6.m2aadec
    0 references
    Q10931
    test
    ∼ asymptotic-expansion {\displaystyle{\displaystyle\sim}}
    xml-id
    C2.S1.SS3.p1.m11acdec
    0 references
     
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