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DLMF:7.6.E10 - MaRDI portal

DLMF:7.6.E10 (Q3067)

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DLMF:7.6.E10
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    Statements

    DLMF defining formula
    C ⁡ ( z ) = z ⁢ ∑ n = 0 ∞ 𝗃 2 ⁢ n ⁡ ( 1 2 ⁢ π ⁢ z 2 ) , Fresnel-cosine-integral 𝑧 𝑧 superscript subscript 𝑛 0 spherical-Bessel-J 2 𝑛 1 2 𝜋 superscript 𝑧 2 {\displaystyle{\displaystyle C\left(z\right)=z\sum_{n=0}^{\infty}\mathsf{j}_{2% n}\left(\tfrac{1}{2}\pi z^{2}\right),}}
    0 references
    Symbols used
    Fresnel integral
    DLMF defining formula
    C ⁡ ( z ) Fresnel-cosine-integral 𝑧 {\displaystyle{\displaystyle C\left(\NVar{z}\right)}}
    xml-id
    C7.S2.E7.m2abdec
    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.m2ahdec
    0 references
    spherical Bessel function of the first kind
    DLMF defining formula
    𝗃 n ⁡ ( z ) spherical-Bessel-J 𝑛 𝑧 {\displaystyle{\displaystyle\mathsf{j}_{\NVar{n}}\left(\NVar{z}\right)}}
    xml-id
    C10.S47.E3.m2adec
    0 references
    complex variable
    DLMF defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C7.S1.XMD2.m1idec
    0 references
    nonnegative integer
    DLMF defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C7.S1.XMD3.m1idec
    0 references

    Identifiers

     
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