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DLMF:7.6.E3 - MaRDI portal

DLMF:7.6.E3 (Q3060)

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DLMF:7.6.E3
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    Statements

    DLMF defining formula
    w ⁡ ( z ) = ∑ n = 0 ∞ ( i ⁢ z ) n Γ ⁡ ( 1 2 ⁢ n + 1 ) . error-function-w 𝑧 superscript subscript 𝑛 0 superscript 𝑖 𝑧 𝑛 Euler-Gamma 1 2 𝑛 1 {\displaystyle{\displaystyle w\left(z\right)=\sum_{n=0}^{\infty}\frac{(iz)^{n}% }{\Gamma\left(\frac{1}{2}n+1\right)}.}}
    0 references
    Symbols used
    gamma function
    DLMF defining formula
    Γ ⁡ ( z ) Euler-Gamma 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
    xml-id
    C5.S2.E1.m2adec
    0 references
    Faddeeva (or Faddeyeva) function
    DLMF defining formula
    w ⁡ ( z ) error-function-w 𝑧 {\displaystyle{\displaystyle w\left(\NVar{z}\right)}}
    xml-id
    C7.S2.E3.m2adec
    0 references
    imaginary unit
    DLMF defining formula
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    xml-id
    C1.S9.E1.m2adec
    0 references
    complex variable
    DLMF defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C7.S1.XMD2.m1bdec
    0 references
    nonnegative integer
    DLMF defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C7.S1.XMD3.m1bdec
    0 references

    Identifiers

     
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