DLMF:11.11.E15 (Q4081): Difference between revisions

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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.m2aadec

Revision as of 14:02, 2 January 2020

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DLMF:11.11.E15
No description defined

    Statements

    test
    𝐀 - ν ⁡ ( λ ⁢ ν ) ∼ ( 2 π ⁢ ν ) 1 / 2 ⁢ ( 1 + 1 - λ 2 λ ) ν ⁢ e - ν ⁢ 1 - λ 2 ( 1 - λ 2 ) 1 / 4 , asymptotically-equals associated-Anger-Weber-A 𝜈 𝜆 𝜈 superscript 2 𝜋 𝜈 1 2 superscript 1 1 superscript 𝜆 2 𝜆 𝜈 superscript 𝑒 𝜈 1 superscript 𝜆 2 superscript 1 superscript 𝜆 2 1 4 {\displaystyle{\displaystyle\mathbf{A}_{-\nu}\left(\lambda\nu\right)\sim\left(% \frac{2}{\pi\nu}\right)^{1/2}\left(\frac{1+\sqrt{1-\lambda^{2}}}{\lambda}% \right)^{\nu}\frac{e^{-\nu\sqrt{1-\lambda^{2}}}}{(1-\lambda^{2})^{1/4}},}}
    0 references
    DLMF id
    DLMF:11.11.E15
    0 references
    constraint
    0 < λ < 1 0 𝜆 1 {\displaystyle{\displaystyle 0<\lambda<1}}
    0 references
    Symbols used
    Anger–Weber function
    test
    𝐀 ν ⁡ ( z ) associated-Anger-Weber-A 𝜈 𝑧 {\displaystyle{\displaystyle\mathbf{A}_{\NVar{\nu}}\left(\NVar{z}\right)}}
    xml-id
    C11.S10.E4.m2aedec
    0 references
    asymptotic equality
    test
    ∼ asymptotically-equals {\displaystyle{\displaystyle\sim}}
    xml-id
    C2.S1.E1.m2abdec
    0 references
    the ratio of the circumference of a circle to its diameter
    test
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2ajdec
    0 references
    base of natural logarithm
    test
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2aadec
    0 references
     
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