DLMF:7.6.E9 (Q2368)

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DLMF:7.6.E9
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    Statements

    Defining formula
    erf ⁡ ( a ⁢ z ) = 2 ⁢ z π ⁢ e ( 1 2 - a 2 ) ⁢ z 2 ⁢ ∑ n = 0 ∞ T 2 ⁢ n + 1 ⁡ ( a ) ⁢ 𝗂 n ( 1 ) ⁡ ( 1 2 ⁢ z 2 ) , error-function 𝑎 𝑧 2 𝑧 𝜋 superscript 𝑒 1 2 superscript 𝑎 2 superscript 𝑧 2 superscript subscript 𝑛 0 Chebyshev-polynomial-first-kind-T 2 𝑛 1 𝑎 spherical-Bessel-I-1 𝑛 1 2 superscript 𝑧 2 {\displaystyle{\displaystyle\operatorname{erf}\left(az\right)=\frac{2z}{\sqrt{% \pi}}e^{(\frac{1}{2}-a^{2})z^{2}}\sum_{n=0}^{\infty}T_{2n+1}\left(a\right){% \mathsf{i}^{(1)}_{n}}\left(\tfrac{1}{2}z^{2}\right),}}
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    DLMF id
    DLMF:7.6.E9
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    constraint
    - 1 ≤ a ≤ 1 1 𝑎 1 {\displaystyle{\displaystyle-1\leq a\leq 1}}
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    Symbols used
    Q11207
    Defining formula
    T n ⁡ ( x ) Chebyshev-polynomial-first-kind-T 𝑛 𝑥 {\displaystyle{\displaystyle T_{\NVar{n}}\left(\NVar{x}\right)}}
    xml-id
    C18.S3.T1.t1.r4.m2adec
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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.m2agdec
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