DLMF:10.22.E28 (Q3402): Difference between revisions

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Changed an Item: Add constraint
Changed an Item: Add constraint
 
(3 intermediate revisions by the same user not shown)
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.m3aaadec
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.m1aodec
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.m1fdec
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.m1rdec

Latest revision as of 01:18, 2 January 2020

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DLMF:10.22.E28
No description defined

    Statements

    0 x t ( J ν - 1 2 ( t ) - J ν + 1 2 ( t ) ) d t = 2 ν J ν 2 ( x ) , superscript subscript 0 𝑥 𝑡 Bessel-J 𝜈 1 2 𝑡 Bessel-J 𝜈 1 2 𝑡 𝑡 2 𝜈 Bessel-J 𝜈 2 𝑥 {\displaystyle{\displaystyle\int_{0}^{x}t\left({J_{\nu-1}^{2}}\left(t\right)-{% J_{\nu+1}^{2}}\left(t\right)\right)\mathrm{d}t=2\nu{J_{\nu}^{2}}\left(x\right)% ,}}
    0 references
    DLMF:10.22.E28
    0 references
    ν > 0 𝜈 0 {\displaystyle{\displaystyle\Re\nu>0}}
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    J ν ( z ) Bessel-J 𝜈 𝑧 {\displaystyle{\displaystyle J_{\NVar{\nu}}\left(\NVar{z}\right)}}
    C10.S2.E2.m2atdec
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    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    C1.S4.SS4.m1aaadec
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    {\displaystyle{\displaystyle\int}}
    C1.S4.SS4.m3aaadec
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    absent {\displaystyle{\displaystyle\Re}}
    C1.S9.E2.m1aodec
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    x 𝑥 {\displaystyle{\displaystyle x}}
    C10.S1.XMD4.m1fdec
    0 references
    ν 𝜈 {\displaystyle{\displaystyle\nu}}
    C10.S1.XMD7.m1rdec
    0 references