DLMF:10.9.E17 (Q3085)

From DRMF
Revision as of 15:15, 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:10.9.E17
No description defined

    Statements

    Defining formula
    J ν ⁡ ( z ) = 1 2 ⁢ π ⁢ i ⁢ ∫ ∞ - π ⁢ i ∞ + π ⁢ i e z ⁢ sinh ⁡ t - ν ⁢ t ⁢ d t , Bessel-J 𝜈 𝑧 1 2 𝜋 𝑖 superscript subscript 𝜋 𝑖 𝜋 𝑖 superscript 𝑒 𝑧 𝑡 𝜈 𝑡 𝑡 {\displaystyle{\displaystyle J_{\nu}\left(z\right)=\frac{1}{2\pi i}\int_{% \infty-\pi i}^{\infty+\pi i}e^{z\sinh t-\nu t}\mathrm{d}t,}}
    0 references
    DLMF id
    DLMF:10.9.E17
    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.m2ahdec
    0 references
    the ratio of the circumference of a circle to its diameter
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2apdec
    0 references
    Q10770
    Defining formula
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1apdec
    0 references
    base of natural logarithm
    Defining formula
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2ajdec
    0 references
    hyperbolic sine function
    Defining formula
    sinh ⁡ z 𝑧 {\displaystyle{\displaystyle\sinh\NVar{z}}}
    xml-id
    C4.S28.E1.m2afdec
    0 references
    imaginary unit
    Defining formula
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    xml-id
    C1.S9.E1.m2aedec
    0 references
    Q10771
    Defining formula
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3apdec
    0 references
    Q11426
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C10.S1.XMD6.m1mdec
    0 references
    Q11427
    Defining formula
    ν 𝜈 {\displaystyle{\displaystyle\nu}}
    xml-id
    C10.S1.XMD7.m1ldec
    0 references
     
        Retrieved from "https://drmf-beta.wmflabs.org/index.php?title=Item:Q3085&oldid=55908"