DLMF:16.11.E1 (Q5233)

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DLMF:16.11.E1
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    Statements

    Defining formula
    E p , q ⁢ ( z ) = ( 2 ⁢ π ) ( p - q ) / 2 ⁢ κ - ν - ( 1 / 2 ) ⁢ e κ ⁢ z 1 / κ ⁢ ∑ k = 0 ∞ c k ⁢ ( κ ⁢ z 1 / κ ) ν - k , subscript 𝐸 𝑝 𝑞 𝑧 superscript 2 𝜋 𝑝 𝑞 2 superscript 𝜅 𝜈 1 2 𝜅 superscript 𝑧 1 𝜅 superscript subscript 𝑘 0 subscript 𝑐 𝑘 superscript 𝜅 superscript 𝑧 1 𝜅 𝜈 𝑘 {\displaystyle{\displaystyle E_{p,q}(z)=(2\pi)^{\ifrac{(p-q)}{2}}\kappa^{-\nu-% (\ifrac{1}{2})}{\mathrm{e}^{\kappa z^{\ifrac{1}{\kappa}}}}\sum_{k=0}^{\infty}c% _{k}\left(\kappa z^{\ifrac{1}{\kappa}}\right)^{\nu-k},}}
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    DLMF id
    DLMF:16.11.E1
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    constraint
    p < q + 1 𝑝 𝑞 1 {\displaystyle{\displaystyle p<q+1}}
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    Symbols used
    the ratio of the circumference of a circle to its diameter
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2adec
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    base of natural logarithm
    Defining formula
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2adec
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    Q11690
    Defining formula
    p 𝑝 {\displaystyle{\displaystyle p}}
    xml-id
    C16.S1.XMD1.m1dec
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    Q11691
    Defining formula
    q 𝑞 {\displaystyle{\displaystyle q}}
    xml-id
    C16.S1.XMD2.m1dec
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    Q11692
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C16.S1.XMD3.m1dec
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    Q11706
    Defining formula
    κ 𝜅 {\displaystyle{\displaystyle\kappa}}
    xml-id
    C16.S11.XMD3.m1dec
    0 references
    Q11707
    Defining formula
    ν 𝜈 {\displaystyle{\displaystyle\nu}}
    xml-id
    C16.S11.XMD4.m1dec
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