DLMF:10.43.E7 (Q3621): Difference between revisions

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‎Changed an Item: Add constraint
‎Changed an Item: Add constraint
Property / Symbols used
 
Property / Symbols used: Q10770 / rank
 
Normal rank
Property / Symbols used: Q10770 / qualifier
 
Defining formula:

d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}

\diff{\NVar{x}}
Property / Symbols used: Q10770 / qualifier
 
xml-id: C1.S4.SS4.m1afdec

Revision as of 13:59, 2 January 2020

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DLMF:10.43.E7
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    Statements

    Defining formula
    ∫ 0 x e ± t ⁢ t ν ⁢ I ν ⁡ ( t ) ⁢ d t = e ± x ⁢ x ν + 1 2 ⁢ ν + 1 ⁢ ( I ν ⁡ ( x ) ∓ I ν + 1 ⁡ ( x ) ) , superscript subscript 0 𝑥 superscript 𝑒 plus-or-minus 𝑡 superscript 𝑡 𝜈 modified-Bessel-first-kind 𝜈 𝑡 𝑡 superscript 𝑒 plus-or-minus 𝑥 superscript 𝑥 𝜈 1 2 𝜈 1 minus-or-plus modified-Bessel-first-kind 𝜈 𝑥 modified-Bessel-first-kind 𝜈 1 𝑥 {\displaystyle{\displaystyle\int_{0}^{x}e^{\pm t}t^{\nu}I_{\nu}\left(t\right)% \mathrm{d}t=\frac{e^{\pm x}x^{\nu+1}}{2\nu+1}(I_{\nu}\left(x\right)\mp I_{\nu+% 1}\left(x\right)),}}
    0 references
    DLMF id
    DLMF:10.43.E7
    0 references
    constraint
    ℜ ⁡ ν > - 1 2 𝜈 1 2 {\displaystyle{\displaystyle\Re\nu>-\tfrac{1}{2}}}
    0 references
    Symbols used
    Q10770
    Defining formula
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1afdec
    0 references
     
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