DLMF:11.6.E5 (Q3981): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: asymptotic equality / rank
 
Normal rank
Property / Symbols used: asymptotic equality / qualifier
 
test:

∼ asymptotically-equals {\displaystyle{\displaystyle\sim}}

\asympeq
Property / Symbols used: asymptotic equality / qualifier
 
xml-id: C2.S1.E1.m2adec
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.m2addec
Property / Symbols used
 
Property / Symbols used: base of natural logarithm / rank
 
Normal rank
Property / Symbols used: base of natural logarithm / qualifier
 
test:

e {\displaystyle{\displaystyle\mathrm{e}}}

\expe
Property / Symbols used: base of natural logarithm / qualifier
 
xml-id: C4.S2.E11.m2adec
Property / Symbols used
 
Property / Symbols used: modified Struve function / rank
 
Normal rank
Property / Symbols used: modified Struve function / qualifier
 
test:

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

\modStruveL{\NVar{\nu}}@{\NVar{z}}
Property / Symbols used: modified Struve function / qualifier
 
xml-id: C11.S2.E2.m2adec
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.m1addec
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.m1ddec
Property / Symbols used
 
Property / Symbols used: Q11492 / rank
 
Normal rank
Property / Symbols used: Q11492 / qualifier
 
test:

ν 𝜈 {\displaystyle{\displaystyle\nu}}

\nu
Property / Symbols used: Q11492 / qualifier
 
xml-id: C11.S1.XMD3.m1bdec
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.m1ddec

Latest revision as of 13:47, 2 January 2020

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English
DLMF:11.6.E5
No description defined

    Statements

    test
    𝐇 ν ⁡ ( z ) , 𝐋 ν ⁡ ( z ) ∼ z π ⁢ ν ⁢ 2 ⁢ ( e ⁢ z 2 ⁢ ν ) ν , asymptotically-equals Struve-H 𝜈 𝑧 modified-Struve-L 𝜈 𝑧 𝑧 𝜋 𝜈 2 superscript 𝑒 𝑧 2 𝜈 𝜈 {\displaystyle{\displaystyle\mathbf{H}_{\nu}\left(z\right),\mathbf{L}_{\nu}% \left(z\right)\sim\frac{z}{\pi\nu\sqrt{2}}\left(\frac{ez}{2\nu}\right)^{\nu},}}
    0 references
    DLMF id
    DLMF:11.6.E5
    0 references
    constraint
    | ph ⁡ ν | ≤ π - δ phase 𝜈 𝜋 𝛿 {\displaystyle{\displaystyle|\operatorname{ph}\nu|\leq\pi-\delta}}
    0 references
    Symbols used
    Struve function
    test
    𝐇 ν ⁡ ( z ) Struve-H 𝜈 𝑧 {\displaystyle{\displaystyle\mathbf{H}_{\NVar{\nu}}\left(\NVar{z}\right)}}
    xml-id
    C11.S2.E1.m2adec
    0 references
    asymptotic equality
    test
    ∼ asymptotically-equals {\displaystyle{\displaystyle\sim}}
    xml-id
    C2.S1.E1.m2adec
    0 references
    the ratio of the circumference of a circle to its diameter
    test
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2addec
    0 references
    base of natural logarithm
    test
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2adec
    0 references
    modified Struve function
    test
    𝐋 ν ⁡ ( z ) modified-Struve-L 𝜈 𝑧 {\displaystyle{\displaystyle\mathbf{L}_{\NVar{\nu}}\left(\NVar{z}\right)}}
    xml-id
    C11.S2.E2.m2adec
    0 references
    Q10817
    test
    ph phase {\displaystyle{\displaystyle\operatorname{ph}}}
    xml-id
    C1.S9.E7.m1addec
    0 references
    Q11491
    test
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C11.S1.XMD2.m1ddec
    0 references
    Q11492
    test
    ν 𝜈 {\displaystyle{\displaystyle\nu}}
    xml-id
    C11.S1.XMD3.m1bdec
    0 references
    Q11498
    test
    δ 𝛿 {\displaystyle{\displaystyle\delta}}
    xml-id
    C11.S1.XMD6.m1ddec
    0 references
     
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