DLMF:8.21.E17 (Q2739)

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DLMF:8.21.E17
No description defined

    Statements

    test
    Ci ⁡ ( a , z ) = z a ⁢ ∑ k = 0 ∞ ( 2 ⁢ k + 1 2 ) ⁢ ( 1 2 - 1 2 ⁢ a ) k ( 1 2 ⁢ a ) k + 1 ⁢ 𝗃 2 ⁢ k ⁡ ( z ) , generalized-cosine-integral-Ci 𝑎 𝑧 superscript 𝑧 𝑎 superscript subscript 𝑘 0 2 𝑘 1 2 Pochhammer 1 2 1 2 𝑎 𝑘 Pochhammer 1 2 𝑎 𝑘 1 spherical-Bessel-J 2 𝑘 𝑧 {\displaystyle{\displaystyle\mathrm{Ci}\left(a,z\right)=z^{a}\sum_{k=0}^{% \infty}\frac{\left(2k+\frac{1}{2}\right){\left(\frac{1}{2}-\frac{1}{2}a\right)% _{k}}}{{\left(\frac{1}{2}a\right)_{k+1}}}\mathsf{j}_{2k}\left(z\right),}}
    0 references
    DLMF id
    DLMF:8.21.E17
    0 references
    constraint
    a ≠ 0 , - 2 , - 4 , … 𝑎 0 2 4 … {\displaystyle{\displaystyle a\neq 0,-2,-4,\dots}}
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    Symbols used
    Q10759
    test
    ( a ) n Pochhammer 𝑎 𝑛 {\displaystyle{\displaystyle{\left(\NVar{a}\right)_{\NVar{n}}}}}
    xml-id
    C5.S2.SS3.m1aadec
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    generalized cosine integral
    test
    Ci ⁡ ( a , z ) generalized-cosine-integral-Ci 𝑎 𝑧 {\displaystyle{\displaystyle\mathrm{Ci}\left(\NVar{a},\NVar{z}\right)}}
    xml-id
    C8.S21.E2.m2aedec
    0 references
    spherical Bessel function of the first kind
    test
    𝗃 n ⁡ ( z ) spherical-Bessel-J 𝑛 𝑧 {\displaystyle{\displaystyle\mathsf{j}_{\NVar{n}}\left(\NVar{z}\right)}}
    xml-id
    C10.S47.E3.m2aadec
    0 references
    Q11323
    test
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C8.S1.XMD2.m1mdec
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    Q11324
    test
    a 𝑎 {\displaystyle{\displaystyle a}}
    xml-id
    C8.S1.XMD3.m1ndec
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    Q11330
    test
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C8.S1.XMD5.m1cdec
    0 references
     
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