DLMF:11.10.E33 (Q4752)

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DLMF:11.10.E33
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    Statements

    DLMF defining formula
    𝐄 ν - 1 ⁡ ( z ) + 𝐄 ν + 1 ⁡ ( z ) = 2 ⁢ ν z ⁢ 𝐄 ν ⁡ ( z ) - 2 π ⁢ z ⁢ ( 1 - cos ⁡ ( π ⁢ ν ) ) . Weber-E 𝜈 1 𝑧 Weber-E 𝜈 1 𝑧 2 𝜈 𝑧 Weber-E 𝜈 𝑧 2 𝜋 𝑧 1 𝜋 𝜈 {\displaystyle{\displaystyle\mathbf{E}_{\nu-1}\left(z\right)+\mathbf{E}_{\nu+1% }\left(z\right)=\frac{2\nu}{z}\mathbf{E}_{\nu}\left(z\right)-\frac{2}{\pi z}(1% -\cos\left(\pi\nu\right)).}}
    0 references
    Symbols used
    Weber function
    DLMF defining formula
    𝐄 ν ⁡ ( z ) Weber-E 𝜈 𝑧 {\displaystyle{\displaystyle\mathbf{E}_{\NVar{\nu}}\left(\NVar{z}\right)}}
    xml-id
    C11.S10.E2.m2asdec
    0 references
    the ratio of the circumference of a circle to its diameter
    DLMF defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2azdec
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    cosine function
    DLMF defining formula
    cos ⁡ z 𝑧 {\displaystyle{\displaystyle\cos\NVar{z}}}
    xml-id
    C4.S14.E2.m2andec
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    complex variable
    DLMF defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C11.S1.XMD2.m1addec
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    real or complex order
    DLMF defining formula
    ν 𝜈 {\displaystyle{\displaystyle\nu}}
    xml-id
    C11.S1.XMD3.m1abdec
    0 references

    Identifiers

     
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