DLMF:10.22.E32 (Q3406): Difference between revisions

From DRMF
Jump to navigation Jump to search
← Older editNewer edit →
‎Changed an Item: Add constraint
‎Changed an Item: Add constraint
Property / Symbols used
 
Property / Symbols used: Q11435 / rank
 
Normal rank
Property / Symbols used: Q11435 / qualifier
 
Defining formula:

x 𝑥 {\displaystyle{\displaystyle x}}

x
Property / Symbols used: Q11435 / qualifier
 
xml-id: C10.S1.XMD4.m1jdec

Revision as of 13:18, 2 January 2020

No description defined
Language Label Description Also known as
English
DLMF:10.22.E32
No description defined

    Statements

    Defining formula
    ∫ 0 x J ν ⁡ ( t ) ⁢ J 1 - ν ⁡ ( x - t ) ⁢ d t = J 0 ⁡ ( x ) - cos ⁡ x , superscript subscript 0 𝑥 Bessel-J 𝜈 𝑡 Bessel-J 1 𝜈 𝑥 𝑡 𝑡 Bessel-J 0 𝑥 𝑥 {\displaystyle{\displaystyle\int_{0}^{x}J_{\nu}\left(t\right)J_{1-\nu}\left(x-% t\right)\mathrm{d}t=J_{0}\left(x\right)-\cos x,}}
    0 references
    DLMF id
    DLMF:10.22.E32
    0 references
    constraint
    - 1 < ℜ ⁡ ν < 2 1 𝜈 2 {\displaystyle{\displaystyle-1<\Re\nu<2}}
    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.m2axdec
    0 references
    cosine function
    Defining formula
    cos ⁡ z 𝑧 {\displaystyle{\displaystyle\cos\NVar{z}}}
    xml-id
    C4.S14.E2.m2amdec
    0 references
    Q10770
    Defining formula
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1aaedec
    0 references
    Q10771
    Defining formula
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3aaedec
    0 references
    Q10811
    Defining formula
    ℜ ⁡ absent {\displaystyle{\displaystyle\Re}}
    xml-id
    C1.S9.E2.m1aqdec
    0 references
    Q11435
    Defining formula
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C10.S1.XMD4.m1jdec
    0 references
     
        Retrieved from "https://drmf-beta.wmflabs.org/index.php?title=Item:Q3406&oldid=35516"