DLMF:10.22.E27 (Q3401)

From DRMF
Revision as of 01:18, 2 January 2020 by Admin (talk | contribs) (‎Changed an Item: Add constraint)
Jump to navigation Jump to search
No description defined
Language Label Description Also known as
English
DLMF:10.22.E27
No description defined

    Statements

    Defining formula
    ∫ 0 x t ⁢ J ν - 1 2 ⁡ ( t ) ⁢ d t = 2 ⁢ ∑ k = 0 ∞ ( ν + 2 ⁢ k ) ⁢ J ν + 2 ⁢ k 2 ⁡ ( x ) , superscript subscript 0 𝑥 𝑡 Bessel-J 𝜈 1 2 𝑡 𝑡 2 superscript subscript 𝑘 0 𝜈 2 𝑘 Bessel-J 𝜈 2 𝑘 2 𝑥 {\displaystyle{\displaystyle\int_{0}^{x}t{J_{\nu-1}^{2}}\left(t\right)\mathrm{% d}t=2\sum_{k=0}^{\infty}(\nu+2k){J_{\nu+2k}^{2}}\left(x\right),}}
    0 references
    DLMF id
    DLMF:10.22.E27
    0 references
    constraint
    ℜ ⁡ ν > 0 𝜈 0 {\displaystyle{\displaystyle\Re\nu>0}}
    0 references
    Symbols used
    Bessel function of the first kind
    Defining formula
    J ν ⁡ ( z ) Bessel-J 𝜈 𝑧 {\displaystyle{\displaystyle J_{\NVar{\nu}}\left(\NVar{z}\right)}}
    xml-id
    C10.S2.E2.m2asdec
    0 references
    Q10770
    Defining formula
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1azdec
    0 references
    Q10771
    Defining formula
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3azdec
    0 references
    Q10811
    Defining formula
    ℜ ⁡ absent {\displaystyle{\displaystyle\Re}}
    xml-id
    C1.S9.E2.m1andec
    0 references
    Q11428
    Defining formula
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C10.S1.XMD3.m1edec
    0 references
     
        Retrieved from "https://drmf-beta.wmflabs.org/index.php?title=Item:Q3401&oldid=30308"