DLMF:8.21.E16 (Q2738)

From DRMF
Revision as of 14:17, 2 January 2020 by Admin (talk | contribs) (‎Changed an Item: Add constraint)
(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)
Jump to navigation Jump to search
No description defined
Language Label Description Also known as
English
DLMF:8.21.E16
No description defined

    Statements

    Defining formula
    Si ⁡ ( a , z ) = z a ⁢ ∑ k = 0 ∞ ( 2 ⁢ k + 3 2 ) ⁢ ( 1 - 1 2 ⁢ a ) k ( 1 2 + 1 2 ⁢ a ) k + 1 ⁢ 𝗃 2 ⁢ k + 1 ⁡ ( z ) , generalized-sine-integral-Si 𝑎 𝑧 superscript 𝑧 𝑎 superscript subscript 𝑘 0 2 𝑘 3 2 Pochhammer 1 1 2 𝑎 𝑘 Pochhammer 1 2 1 2 𝑎 𝑘 1 spherical-Bessel-J 2 𝑘 1 𝑧 {\displaystyle{\displaystyle\mathrm{Si}\left(a,z\right)=z^{a}\sum_{k=0}^{% \infty}\frac{\left(2k+\frac{3}{2}\right){\left(1-\frac{1}{2}a\right)_{k}}}{{% \left(\frac{1}{2}+\frac{1}{2}a\right)_{k+1}}}\mathsf{j}_{2k+1}\left(z\right),}}
    0 references
    DLMF id
    DLMF:8.21.E16
    0 references
    constraint
    a ≠ - 1 , - 3 , - 5 , … 𝑎 1 3 5 … {\displaystyle{\displaystyle a\neq-1,-3,-5,\dots}}
    0 references
    Symbols used
    Q10759
    Defining formula
    ( a ) n Pochhammer 𝑎 𝑛 {\displaystyle{\displaystyle{\left(\NVar{a}\right)_{\NVar{n}}}}}
    xml-id
    C5.S2.SS3.m1adec
    0 references
    generalized sine integral
    Defining formula
    Si ⁡ ( a , z ) generalized-sine-integral-Si 𝑎 𝑧 {\displaystyle{\displaystyle\mathrm{Si}\left(\NVar{a},\NVar{z}\right)}}
    xml-id
    C8.S21.E2.m3afdec
    0 references
    spherical Bessel function of the first kind
    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
    Q11323
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C8.S1.XMD2.m1ldec
    0 references
    Q11324
    Defining formula
    a 𝑎 {\displaystyle{\displaystyle a}}
    xml-id
    C8.S1.XMD3.m1mdec
    0 references
    Q11330
    Defining formula
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C8.S1.XMD5.m1bdec
    0 references
     
        Retrieved from "https://drmf-beta.wmflabs.org/index.php?title=Item:Q2738&oldid=45565"