DLMF:11.10.E16 (Q4034): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: cosine function / rank
 
Normal rank
Property / Symbols used: cosine function / qualifier
 
Defining formula:

cos ⁡ z 𝑧 {\displaystyle{\displaystyle\cos\NVar{z}}}

\cos@@{\NVar{z}}
Property / Symbols used: cosine function / qualifier
 
xml-id: C4.S14.E2.m2agdec
Property / Symbols used
 
Property / Symbols used: Q11491 / rank
 
Normal rank
Property / Symbols used: Q11491 / qualifier
 
Defining formula:

z 𝑧 {\displaystyle{\displaystyle z}}

z
Property / Symbols used: Q11491 / qualifier
 
xml-id: C11.S1.XMD2.m1odec
Property / Symbols used
 
Property / Symbols used: Q11492 / rank
 
Normal rank
Property / Symbols used: Q11492 / qualifier
 
Defining formula:

ν 𝜈 {\displaystyle{\displaystyle\nu}}

\nu
Property / Symbols used: Q11492 / qualifier
 
xml-id: C11.S1.XMD3.m1sdec

Latest revision as of 14:56, 2 January 2020

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DLMF:11.10.E16
No description defined

    Statements

    Defining formula
    𝐄 ν ⁡ ( z ) = - Y ν ⁡ ( z ) - cos ⁡ ( π ⁢ ν ) ⁢ 𝐀 ν ⁡ ( z ) - 𝐀 - ν ⁡ ( z ) . Weber-E 𝜈 𝑧 Bessel-Y-Weber 𝜈 𝑧 𝜋 𝜈 associated-Anger-Weber-A 𝜈 𝑧 associated-Anger-Weber-A 𝜈 𝑧 {\displaystyle{\displaystyle\mathbf{E}_{\nu}\left(z\right)=-Y_{\nu}\left(z% \right)-\cos\left(\pi\nu\right)\,\mathbf{A}_{\nu}\left(z\right)-\mathbf{A}_{-% \nu}\left(z\right).}}
    0 references
    DLMF id
    DLMF:11.10.E16
    0 references
    Symbols used
    Bessel function of the second kind
    Defining formula
    Y ν ⁡ ( z ) Bessel-Y-Weber 𝜈 𝑧 {\displaystyle{\displaystyle Y_{\NVar{\nu}}\left(\NVar{z}\right)}}
    xml-id
    C10.S2.E3.m2adec
    0 references
    Weber function
    Defining formula
    𝐄 ν ⁡ ( z ) Weber-E 𝜈 𝑧 {\displaystyle{\displaystyle\mathbf{E}_{\NVar{\nu}}\left(\NVar{z}\right)}}
    xml-id
    C11.S10.E2.m2aidec
    0 references
    Anger–Weber function
    Defining formula
    𝐀 ν ⁡ ( z ) associated-Anger-Weber-A 𝜈 𝑧 {\displaystyle{\displaystyle\mathbf{A}_{\NVar{\nu}}\left(\NVar{z}\right)}}
    xml-id
    C11.S10.E4.m2abdec
    0 references
    the ratio of the circumference of a circle to its diameter
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2akdec
    0 references
    cosine function
    Defining formula
    cos ⁡ z 𝑧 {\displaystyle{\displaystyle\cos\NVar{z}}}
    xml-id
    C4.S14.E2.m2agdec
    0 references
    Q11491
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C11.S1.XMD2.m1odec
    0 references
    Q11492
    Defining formula
    ν 𝜈 {\displaystyle{\displaystyle\nu}}
    xml-id
    C11.S1.XMD3.m1sdec
    0 references
     
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