DLMF:10.23.E21 (Q3475): Difference between revisions

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‎Changed an Item: Add constraint
‎Changed an Item: Add constraint
Property / Symbols used
 
Property / Symbols used: Q11438 / rank
 
Normal rank
Property / Symbols used: Q11438 / qualifier
 
Defining formula:

m 𝑚 {\displaystyle{\displaystyle m}}

m
Property / Symbols used: Q11438 / qualifier
 
xml-id: C10.S1.XMD1.m1bdec

Revision as of 13:33, 2 January 2020

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DLMF:10.23.E21
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    Statements

    Defining formula
    x ν = ∑ m = 1 ∞ 2 ⁢ J ν ⁡ ( j ν , m ⁢ x ) j ν , m ⁢ J ν + 1 ⁡ ( j ν , m ) , superscript 𝑥 𝜈 superscript subscript 𝑚 1 2 Bessel-J 𝜈 subscript 𝑗 𝜈 𝑚 𝑥 zero-Bessel-J 𝜈 𝑚 Bessel-J 𝜈 1 subscript 𝑗 𝜈 𝑚 {\displaystyle{\displaystyle x^{\nu}=\sum_{m=1}^{\infty}\frac{2J_{\nu}\left(j_% {\nu,m}x\right)}{j_{\nu,m}J_{\nu+1}\left(j_{\nu,m}\right)},}}
    0 references
    DLMF id
    DLMF:10.23.E21
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    constraint
    ν > 0 , 0 ≤ x < 1 formulae-sequence 𝜈 0 0 𝑥 1 {\displaystyle{\displaystyle\nu>0,0\leq x<1}}
    0 references
    Symbols used
    Bessel function of the first kind
    Defining formula
    J ν ⁡ ( z ) Bessel-J 𝜈 𝑧 {\displaystyle{\displaystyle J_{\NVar{\nu}}\left(\NVar{z}\right)}}
    xml-id
    C10.S2.E2.m2aodec
    0 references
    Q11456
    Defining formula
    j ν , m zero-Bessel-J 𝜈 𝑚 {\displaystyle{\displaystyle j_{\NVar{\nu},\NVar{m}}}}
    xml-id
    C10.S21.SS1.p2.m11aadec
    0 references
    Q11438
    Defining formula
    m 𝑚 {\displaystyle{\displaystyle m}}
    xml-id
    C10.S1.XMD1.m1bdec
    0 references
     
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