DLMF:10.22.E28 (Q3402)

From DRMF
Jump to navigation Jump to search
No description defined
Language Label Description Also known as
English
DLMF:10.22.E28
No description defined

    Statements

    Defining formula
    ∫ 0 x t ⁢ ( J ν - 1 2 ⁡ ( t ) - J ν + 1 2 ⁡ ( t ) ) ⁢ d t = 2 ⁢ ν ⁢ J ν 2 ⁡ ( x ) , superscript subscript 0 𝑥 𝑡 Bessel-J 𝜈 1 2 𝑡 Bessel-J 𝜈 1 2 𝑡 𝑡 2 𝜈 Bessel-J 𝜈 2 𝑥 {\displaystyle{\displaystyle\int_{0}^{x}t\left({J_{\nu-1}^{2}}\left(t\right)-{% J_{\nu+1}^{2}}\left(t\right)\right)\mathrm{d}t=2\nu{J_{\nu}^{2}}\left(x\right)% ,}}
    0 references
    DLMF id
    DLMF:10.22.E28
    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.m2atdec
    0 references
    Q10770
    Defining formula
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1aaadec
    0 references
    Q10771
    Defining formula
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3aaadec
    0 references
    Q10811
    Defining formula
    ℜ ⁡ absent {\displaystyle{\displaystyle\Re}}
    xml-id
    C1.S9.E2.m1aodec
    0 references
    Q11435
    Defining formula
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C10.S1.XMD4.m1fdec
    0 references
    Q11427
    Defining formula
    ν 𝜈 {\displaystyle{\displaystyle\nu}}
    xml-id
    C10.S1.XMD7.m1rdec
    0 references
     
        Retrieved from "https://drmf-beta.wmflabs.org/index.php?title=Item:Q3402&oldid=30343"