DLMF:11.10.E19 (Q4037)

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DLMF:11.10.E19
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    Statements

    Defining formula
    𝐉 - 1 2 ⁡ ( z ) = 𝐄 1 2 ⁡ ( z ) = ( 1 2 ⁢ π ⁢ z ) - 1 2 ⁢ ( A + ⁢ ( χ ) ⁢ cos ⁡ z - A - ⁢ ( χ ) ⁢ sin ⁡ 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)\cos z-A_{-}(\chi)\sin z),}}
    0 references
    DLMF id
    DLMF:11.10.E19
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    Symbols used
    Anger function
    Defining formula
    𝐉 ν ⁡ ( z ) Anger-J 𝜈 𝑧 {\displaystyle{\displaystyle\mathbf{J}_{\NVar{\nu}}\left(\NVar{z}\right)}}
    xml-id
    C11.S10.E1.m2akdec
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    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.m2akdec
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    the ratio of the circumference of a circle to its diameter
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2andec
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    cosine function
    Defining formula
    cos ⁡ z 𝑧 {\displaystyle{\displaystyle\cos\NVar{z}}}
    xml-id
    C4.S14.E2.m2aidec
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    sine function
    Defining formula
    sin ⁡ z 𝑧 {\displaystyle{\displaystyle\sin\NVar{z}}}
    xml-id
    C4.S14.E1.m2ajdec
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    Q11491
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C11.S1.XMD2.m1rdec
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