DLMF:10.32.E1 (Q3521): Difference between revisions

From DRMF
Jump to navigation Jump to search
Changed an Item: Add constraint
Changed an Item: Add constraint
 
(One intermediate revision by the same user not shown)
Property / Symbols used
 
Property / Symbols used: modified Bessel function of the first kind / rank
 
Normal rank
Property / Symbols used: modified Bessel function of the first kind / qualifier
 
Defining formula:

I ν ( z ) modified-Bessel-first-kind 𝜈 𝑧 {\displaystyle{\displaystyle I_{\NVar{\nu}}\left(\NVar{z}\right)}}

\modBesselI{\NVar{\nu}}@{\NVar{z}}
Property / Symbols used: modified Bessel function of the first kind / qualifier
 
xml-id: C10.S25.E2.m2adec
Property / Symbols used
 
Property / Symbols used: Q11426 / rank
 
Normal rank
Property / Symbols used: Q11426 / qualifier
 
Defining formula:

z 𝑧 {\displaystyle{\displaystyle z}}

z
Property / Symbols used: Q11426 / qualifier
 
xml-id: C10.S1.XMD6.m1dec

Latest revision as of 13:40, 2 January 2020

No description defined
Language Label Description Also known as
English
DLMF:10.32.E1
No description defined

    Statements

    I 0 ( z ) = 1 π 0 π e ± z cos θ d θ = 1 π 0 π cosh ( z cos θ ) d θ . modified-Bessel-first-kind 0 𝑧 1 𝜋 superscript subscript 0 𝜋 superscript 𝑒 plus-or-minus 𝑧 𝜃 𝜃 1 𝜋 superscript subscript 0 𝜋 𝑧 𝜃 𝜃 {\displaystyle{\displaystyle I_{0}\left(z\right)=\frac{1}{\pi}\int_{0}^{\pi}e^% {\pm z\cos\theta}\mathrm{d}\theta=\frac{1}{\pi}\int_{0}^{\pi}\cosh\left(z\cos% \theta\right)\mathrm{d}\theta.}}
    0 references
    DLMF:10.32.E1
    0 references
    π {\displaystyle{\displaystyle\pi}}
    C3.S12.E1.m2adec
    0 references
    cos z 𝑧 {\displaystyle{\displaystyle\cos\NVar{z}}}
    C4.S14.E2.m2adec
    0 references
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    C1.S4.SS4.m1adec
    0 references
    e {\displaystyle{\displaystyle\mathrm{e}}}
    C4.S2.E11.m2adec
    0 references
    cosh z 𝑧 {\displaystyle{\displaystyle\cosh\NVar{z}}}
    C4.S28.E2.m2adec
    0 references
    {\displaystyle{\displaystyle\int}}
    C1.S4.SS4.m3adec
    0 references
    I ν ( z ) modified-Bessel-first-kind 𝜈 𝑧 {\displaystyle{\displaystyle I_{\NVar{\nu}}\left(\NVar{z}\right)}}
    C10.S25.E2.m2adec
    0 references
    z 𝑧 {\displaystyle{\displaystyle z}}
    C10.S1.XMD6.m1dec
    0 references