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DLMF:13.29.E3 - MaRDI portal

DLMF:13.29.E3 (Q5367)

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DLMF:13.29.E3
No description defined

    Statements

    DLMF defining formula
    e - 1 2 ⁢ z = ∑ s = 0 ∞ ( 2 ⁢ μ ) s ⁢ ( 1 2 + μ - κ ) s ( 2 ⁢ μ ) 2 ⁢ s ⁢ s ! ⁢ ( - z ) s ⁢ y ⁢ ( s ) , superscript 𝑒 1 2 𝑧 superscript subscript 𝑠 0 Pochhammer 2 𝜇 𝑠 Pochhammer 1 2 𝜇 𝜅 𝑠 Pochhammer 2 𝜇 2 𝑠 𝑠 superscript 𝑧 𝑠 𝑦 𝑠 {\displaystyle{\displaystyle e^{-\frac{1}{2}z}=\sum_{s=0}^{\infty}\frac{{\left% (2\mu\right)_{s}}{\left(\frac{1}{2}+\mu-\kappa\right)_{s}}}{{\left(2\mu\right)% _{2s}}s!}(-z)^{s}y(s),}}
    0 references
    Symbols used
    Q10733
    DLMF defining formula
    ( a ) n Pochhammer 𝑎 𝑛 {\displaystyle{\displaystyle{\left(\NVar{a}\right)_{\NVar{n}}}}}
    xml-id
    C5.S2.SS3.m1adec
    0 references
    base of natural logarithm
    DLMF defining formula
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2adec
    0 references
    Q10729
    DLMF defining formula
    ! {\displaystyle{\displaystyle!}}
    xml-id
    introduction.Sx4.p1.t1.r15.m5adec
    0 references
    nonnegative integer
    DLMF defining formula
    s 𝑠 {\displaystyle{\displaystyle s}}
    xml-id
    C13.S1.XMD3.m1dec
    0 references
    complex variable
    DLMF defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C13.S1.XMD6.m1bdec
    0 references
    solution (locally)
    DLMF defining formula
    y ⁢ ( n ) 𝑦 𝑛 {\displaystyle{\displaystyle y(n)}}
    xml-id
    C13.S29.XMD1.m1bdec
    0 references

    Identifiers

     
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