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

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Property / Symbols used
 
Property / Symbols used: Euler’s constant / rank
 
Normal rank
Property / Symbols used: Euler’s constant / qualifier
 
test:

γ {\displaystyle{\displaystyle\gamma}}

\EulerConstant
Property / Symbols used: Euler’s constant / qualifier
 
xml-id: C5.S2.E3.m2aadec
Property / Symbols used
 
Property / Symbols used: modified Struve function / rank
 
Normal rank
Property / Symbols used: modified Struve function / qualifier
 
test:

𝐌 ν ⁡ ( z ) associated-Struve-M 𝜈 𝑧 {\displaystyle{\displaystyle\mathbf{M}_{\NVar{\nu}}\left(\NVar{z}\right)}}

\modStruveM{\NVar{\nu}}@{\NVar{z}}
Property / Symbols used: modified Struve function / qualifier
 
xml-id: C11.S2.E6.m2aadec
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
Property / Symbols used
 
Property / Symbols used: the ratio of the circumference of a circle to its diameter / rank
 
Normal rank
Property / Symbols used: the ratio of the circumference of a circle to its diameter / qualifier
 
test:

π {\displaystyle{\displaystyle\pi}}

\cpi
Property / Symbols used: the ratio of the circumference of a circle to its diameter / qualifier
 
xml-id: C3.S12.E1.m2acdec
Property / Symbols used
 
Property / Symbols used: Q10770 / rank
 
Normal rank
Property / Symbols used: Q10770 / qualifier
 
test:

d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}

\diff{\NVar{x}}
Property / Symbols used: Q10770 / qualifier
 
xml-id: C1.S4.SS4.m1aadec
Property / Symbols used
 
Property / Symbols used: Q10755 / rank
 
Normal rank
Property / Symbols used: Q10755 / qualifier
 
test:

! {\displaystyle{\displaystyle!}}

!
Property / Symbols used: Q10755 / qualifier
 
xml-id: introduction.Sx4.p1.t1.r15.m5aadec
Property / Symbols used
 
Property / Symbols used: Q10771 / rank
 
Normal rank
Property / Symbols used: Q10771 / qualifier
 
test:

∫ {\displaystyle{\displaystyle\int}}

\int
Property / Symbols used: Q10771 / qualifier
 
xml-id: C1.S4.SS4.m3aadec
Property / Symbols used
 
Property / Symbols used: principal branch of logarithm function / rank
 
Normal rank
Property / Symbols used: principal branch of logarithm function / qualifier
 
test:

ln ⁡ z 𝑧 {\displaystyle{\displaystyle\ln\NVar{z}}}

\ln@@{\NVar{z}}
Property / Symbols used: principal branch of logarithm function / qualifier
 
xml-id: C4.S2.E2.m2aadec
Property / Symbols used
 
Property / Symbols used: Q10817 / rank
 
Normal rank
Property / Symbols used: Q10817 / qualifier
 
test:

ph phase {\displaystyle{\displaystyle\operatorname{ph}}}

\phase
Property / Symbols used: Q10817 / qualifier
 
xml-id: C1.S9.E7.m1acdec
Property / Symbols used
 
Property / Symbols used: Q11491 / rank
 
Normal rank
Property / Symbols used: Q11491 / qualifier
 
test:

z 𝑧 {\displaystyle{\displaystyle z}}

z
Property / Symbols used: Q11491 / qualifier
 
xml-id: C11.S1.XMD2.m1cdec
Property / Symbols used
 
Property / Symbols used: Q11497 / rank
 
Normal rank
Property / Symbols used: Q11497 / qualifier
 
test:

k 𝑘 {\displaystyle{\displaystyle k}}

k
Property / Symbols used: Q11497 / qualifier
 
xml-id: C11.S1.XMD5.m1cdec
Property / Symbols used
 
Property / Symbols used: Q11498 / rank
 
Normal rank
Property / Symbols used: Q11498 / qualifier
 
test:

δ 𝛿 {\displaystyle{\displaystyle\delta}}

\delta
Property / Symbols used: Q11498 / qualifier
 
xml-id: C11.S1.XMD6.m1cdec

Latest revision as of 13:47, 2 January 2020

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DLMF:11.6.E4
No description defined

    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
    the ratio of the circumference of a circle to its diameter
    test
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2acdec
    0 references
    Q10770
    test
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1aadec
    0 references
    Q10755
    test
    ! {\displaystyle{\displaystyle!}}
    xml-id
    introduction.Sx4.p1.t1.r15.m5aadec
    0 references
    Q10771
    test
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3aadec
    0 references
    principal branch of logarithm function
    test
    ln ⁡ z 𝑧 {\displaystyle{\displaystyle\ln\NVar{z}}}
    xml-id
    C4.S2.E2.m2aadec
    0 references
    Q10817
    test
    ph phase {\displaystyle{\displaystyle\operatorname{ph}}}
    xml-id
    C1.S9.E7.m1acdec
    0 references
    Q11491
    test
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C11.S1.XMD2.m1cdec
    0 references
    Q11497
    test
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C11.S1.XMD5.m1cdec
    0 references
    Q11498
    test
    δ 𝛿 {\displaystyle{\displaystyle\delta}}
    xml-id
    C11.S1.XMD6.m1cdec
    0 references
     
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