DLMF:8.21.E17 (Q2739): Difference between revisions

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imported>Admin
Property / constraint
 

a 0 , - 2 , - 4 , 𝑎 0 2 4 {\displaystyle{\displaystyle a\neq 0,-2,-4,\dots}}

a\neq 0,-2,-4,\dots
Property / constraint: a 0 , - 2 , - 4 , 𝑎 0 2 4 {\displaystyle{\displaystyle a\neq 0,-2,-4,\dots}} / rank
 
Normal rank

Revision as of 16:13, 30 December 2019

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DLMF:8.21.E17
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    Statements

    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),}}
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    a 0 , - 2 , - 4 , 𝑎 0 2 4 {\displaystyle{\displaystyle a\neq 0,-2,-4,\dots}}
    0 references