DLMF:10.2.E5 (Q3009): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: asymptotic equality / rank
 
Normal rank
Property / Symbols used: asymptotic equality / qualifier
 
Defining formula:

∼ 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
 
Defining formula:

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.m2abdec
Property / Symbols used
 
Property / Symbols used: base of natural logarithm / rank
 
Normal rank
Property / Symbols used: base of natural logarithm / qualifier
 
Defining formula:

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: imaginary unit / rank
 
Normal rank
Property / Symbols used: imaginary unit / qualifier
 
Defining formula:

i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}

\iunit
Property / Symbols used: imaginary unit / qualifier
 
xml-id: C1.S9.E1.m2adec
Property / Symbols used
 
Property / Symbols used: Q11426 / rank
 
Normal rank
Property / Symbols used: Q11426 / qualifier
 
Defining formula:

z 𝑧 {\displaystyle{\displaystyle z}}

z
Property / Symbols used: Q11426 / qualifier
 
xml-id: C10.S1.XMD6.m1ddec
Property / Symbols used
 
Property / Symbols used: Q11427 / rank
 
Normal rank
Property / Symbols used: Q11427 / qualifier
 
Defining formula:

ν 𝜈 {\displaystyle{\displaystyle\nu}}

\nu
Property / Symbols used: Q11427 / qualifier
 
xml-id: C10.S1.XMD7.m1ddec

Latest revision as of 15:05, 2 January 2020

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English
DLMF:10.2.E5
No description defined

    Statements

    Defining formula
    H ν ( 1 ) ⁡ ( z ) ∼ 2 / ( π ⁢ z ) ⁢ e i ⁢ ( z - 1 2 ⁢ ν ⁢ π - 1 4 ⁢ π ) asymptotically-equals Hankel-H-1-Bessel-third-kind 𝜈 𝑧 2 𝜋 𝑧 superscript 𝑒 𝑖 𝑧 1 2 𝜈 𝜋 1 4 𝜋 {\displaystyle{\displaystyle{H^{(1)}_{\nu}}\left(z\right)\sim\sqrt{2/(\pi z)}e% ^{i(z-\frac{1}{2}\nu\pi-\frac{1}{4}\pi)}}}
    0 references
    DLMF id
    DLMF:10.2.E5
    0 references
    Symbols used
    asymptotic equality
    Defining formula
    ∼ asymptotically-equals {\displaystyle{\displaystyle\sim}}
    xml-id
    C2.S1.E1.m2adec
    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
    base of natural logarithm
    Defining formula
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2adec
    0 references
    imaginary unit
    Defining formula
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    xml-id
    C1.S9.E1.m2adec
    0 references
    Q11426
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C10.S1.XMD6.m1ddec
    0 references
    Q11427
    Defining formula
    ν 𝜈 {\displaystyle{\displaystyle\nu}}
    xml-id
    C10.S1.XMD7.m1ddec
    0 references
     
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