DLMF:11.10.E20 (Q4038): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Q11507 / rank
 
Normal rank
Property / Symbols used: Q11507 / qualifier
 
test:

χ 𝜒 {\displaystyle{\displaystyle\chi}}

\chi
Property / Symbols used: Q11507 / qualifier
 
xml-id: C11.S10.XMD2.m1adec

Latest revision as of 13:57, 2 January 2020

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DLMF:11.10.E20
No description defined

    Statements

    test
    𝐉 1 2 ⁡ ( z ) = - 𝐄 - 1 2 ⁡ ( z ) = ( 1 2 ⁢ π ⁢ z ) - 1 2 ⁢ ( A + ⁢ ( χ ) ⁢ sin ⁡ z + A - ⁢ ( χ ) ⁢ cos ⁡ z ) , Anger-J 1 2 𝑧 Weber-E 1 2 𝑧 superscript 1 2 𝜋 𝑧 1 2 subscript 𝐴 𝜒 𝑧 subscript 𝐴 𝜒 𝑧 {\displaystyle{\displaystyle\mathbf{J}_{\frac{1}{2}}\left(z\right)=-\mathbf{E}% _{-\frac{1}{2}}\left(z\right)\\ =(\tfrac{1}{2}\pi z)^{-\frac{1}{2}}(A_{+}(\chi)\sin z+A_{-}(\chi)\cos z),}}
    0 references
    DLMF id
    DLMF:11.10.E20
    0 references
    Symbols used
    Anger function
    test
    𝐉 ν ⁡ ( z ) Anger-J 𝜈 𝑧 {\displaystyle{\displaystyle\mathbf{J}_{\NVar{\nu}}\left(\NVar{z}\right)}}
    xml-id
    C11.S10.E1.m2aldec
    0 references
    Weber function
    test
    𝐄 ν ⁡ ( z ) Weber-E 𝜈 𝑧 {\displaystyle{\displaystyle\mathbf{E}_{\NVar{\nu}}\left(\NVar{z}\right)}}
    xml-id
    C11.S10.E2.m2aldec
    0 references
    the ratio of the circumference of a circle to its diameter
    test
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2aodec
    0 references
    cosine function
    test
    cos ⁡ z 𝑧 {\displaystyle{\displaystyle\cos\NVar{z}}}
    xml-id
    C4.S14.E2.m2ajdec
    0 references
    sine function
    test
    sin ⁡ z 𝑧 {\displaystyle{\displaystyle\sin\NVar{z}}}
    xml-id
    C4.S14.E1.m2akdec
    0 references
    Q11491
    test
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C11.S1.XMD2.m1sdec
    0 references
    Q11506
    test
    A 𝐴 {\displaystyle{\displaystyle A}}
    xml-id
    C11.S10.XMD1.m1adec
    0 references
    Q11507
    test
    χ 𝜒 {\displaystyle{\displaystyle\chi}}
    xml-id
    C11.S10.XMD2.m1adec
    0 references
     
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