DLMF:10.22.E34 (Q3408): Difference between revisions

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Changed an Item: Add constraint
 
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Property / constraint
 

μ > 0 , ν > - 1 formulae-sequence 𝜇 0 𝜈 1 {\displaystyle{\displaystyle\Re\mu>0,\Re\nu>-1}}

\realpart@@{\mu}>0,\realpart@@{\nu}>-1
Property / constraint: μ > 0 , ν > - 1 formulae-sequence 𝜇 0 𝜈 1 {\displaystyle{\displaystyle\Re\mu>0,\Re\nu>-1}} / rank
 
Normal rank
Property / Symbols used
 
Property / Symbols used: Bessel function of the first kind / rank
 
Normal rank
Property / Symbols used: Bessel function of the first kind / qualifier
 
Defining formula:

J ν ( z ) Bessel-J 𝜈 𝑧 {\displaystyle{\displaystyle J_{\NVar{\nu}}\left(\NVar{z}\right)}}

\BesselJ{\NVar{\nu}}@{\NVar{z}}
Property / Symbols used: Bessel function of the first kind / qualifier
 
xml-id: C10.S2.E2.m2azdec
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.m1aagdec
Property / Symbols used
 
Property / Symbols used: Q10771 / rank
 
Normal rank
Property / Symbols used: Q10771 / qualifier
 
Defining formula:

{\displaystyle{\displaystyle\int}}

\int
Property / Symbols used: Q10771 / qualifier
 
xml-id: C1.S4.SS4.m3aagdec
Property / Symbols used
 
Property / Symbols used: Q10811 / rank
 
Normal rank
Property / Symbols used: Q10811 / qualifier
 
Defining formula:

absent {\displaystyle{\displaystyle\Re}}

\realpart@@
Property / Symbols used: Q10811 / qualifier
 
xml-id: C1.S9.E2.m1asdec
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.m1ldec
Property / Symbols used
 
Property / Symbols used: Q11427 / rank
 
Normal rank
Property / Symbols used: Q11427 / qualifier
 
Defining formula:

ν 𝜈 {\displaystyle{\displaystyle\nu}}

\nu
Property / Symbols used: Q11427 / qualifier
 
xml-id: C10.S1.XMD7.m1vdec

Latest revision as of 13:18, 2 January 2020

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DLMF:10.22.E34
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    Statements

    0 x t - 1 J μ ( t ) J ν ( x - t ) d t = J μ + ν ( x ) μ , superscript subscript 0 𝑥 superscript 𝑡 1 Bessel-J 𝜇 𝑡 Bessel-J 𝜈 𝑥 𝑡 𝑡 Bessel-J 𝜇 𝜈 𝑥 𝜇 {\displaystyle{\displaystyle\int_{0}^{x}t^{-1}J_{\mu}\left(t\right)J_{\nu}% \left(x-t\right)\mathrm{d}t=\frac{J_{\mu+\nu}\left(x\right)}{\mu},}}
    0 references
    DLMF:10.22.E34
    0 references
    μ > 0 , ν > - 1 formulae-sequence 𝜇 0 𝜈 1 {\displaystyle{\displaystyle\Re\mu>0,\Re\nu>-1}}
    0 references
    J ν ( z ) Bessel-J 𝜈 𝑧 {\displaystyle{\displaystyle J_{\NVar{\nu}}\left(\NVar{z}\right)}}
    C10.S2.E2.m2azdec
    0 references
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    C1.S4.SS4.m1aagdec
    0 references
    {\displaystyle{\displaystyle\int}}
    C1.S4.SS4.m3aagdec
    0 references
    absent {\displaystyle{\displaystyle\Re}}
    C1.S9.E2.m1asdec
    0 references
    x 𝑥 {\displaystyle{\displaystyle x}}
    C10.S1.XMD4.m1ldec
    0 references
    ν 𝜈 {\displaystyle{\displaystyle\nu}}
    C10.S1.XMD7.m1vdec
    0 references