DLMF:10.10.E2 (Q3102): Difference between revisions

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Property / constraint
 

ν 0 , - 1 , - 2 , 𝜈 0 1 2 {\displaystyle{\displaystyle\nu\neq 0,-1,-2,\ldots}}

\nu\neq 0,-1,-2,\dotsc
Property / constraint: ν 0 , - 1 , - 2 , 𝜈 0 1 2 {\displaystyle{\displaystyle\nu\neq 0,-1,-2,\ldots}} / 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
 
test:

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.m2aadec
Property / Symbols used
 
Property / Symbols used: Q11426 / rank
 
Normal rank
Property / Symbols used: Q11426 / qualifier
 
test:

z 𝑧 {\displaystyle{\displaystyle z}}

z
Property / Symbols used: Q11426 / qualifier
 
xml-id: C10.S1.XMD6.m1adec
Property / Symbols used
 
Property / Symbols used: Q11427 / rank
 
Normal rank
Property / Symbols used: Q11427 / qualifier
 
test:

ν 𝜈 {\displaystyle{\displaystyle\nu}}

\nu
Property / Symbols used: Q11427 / qualifier
 
xml-id: C10.S1.XMD7.m1adec

Latest revision as of 14:19, 2 January 2020

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DLMF:10.10.E2
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    Statements

    J ν ( z ) J ν - 1 ( z ) = 1 2 z / ν 1 - 1 4 z 2 / ( ν ( ν + 1 ) ) 1 - 1 4 z 2 / ( ( ν + 1 ) ( ν + 2 ) ) 1 - , Bessel-J 𝜈 𝑧 Bessel-J 𝜈 1 𝑧 continued-fraction 1 2 𝑧 𝜈 1 continued-fraction 1 4 superscript 𝑧 2 𝜈 𝜈 1 1 continued-fraction 1 4 superscript 𝑧 2 𝜈 1 𝜈 2 1 {\displaystyle{\displaystyle\frac{J_{\nu}\left(z\right)}{J_{\nu-1}\left(z% \right)}=\cfrac{\tfrac{1}{2}z/\nu}{1-\cfrac{\tfrac{1}{4}z^{2}/(\nu(\nu+1))}{1-% \cfrac{\tfrac{1}{4}z^{2}/((\nu+1)(\nu+2))}{1-\cdots}}},}}
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    ν 0 , - 1 , - 2 , 𝜈 0 1 2 {\displaystyle{\displaystyle\nu\neq 0,-1,-2,\ldots}}
    0 references
    J ν ( z ) Bessel-J 𝜈 𝑧 {\displaystyle{\displaystyle J_{\NVar{\nu}}\left(\NVar{z}\right)}}
    C10.S2.E2.m2aadec
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    z 𝑧 {\displaystyle{\displaystyle z}}
    C10.S1.XMD6.m1adec
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    ν 𝜈 {\displaystyle{\displaystyle\nu}}
    C10.S1.XMD7.m1adec
    0 references