DLMF:33.20.E4 (Q9672): Difference between revisions

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Property / constraint
 

r > 0 𝑟 0 {\displaystyle{\displaystyle r>0}}

r>0
Property / constraint: r > 0 𝑟 0 {\displaystyle{\displaystyle r>0}} / 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: Q12669 / rank
 
Normal rank
Property / Symbols used: Q12669 / qualifier
 
test:

k 𝑘 {\displaystyle{\displaystyle k}}

k
Property / Symbols used: Q12669 / qualifier
 
xml-id: C33.S1.XMD1.m1adec
Property / Symbols used
 
Property / Symbols used: Q12666 / rank
 
Normal rank
Property / Symbols used: Q12666 / qualifier
 
test:

ℓ ℓ {\displaystyle{\displaystyle\ell}}

\ell
Property / Symbols used: Q12666 / qualifier
 
xml-id: C33.S1.XMD2.m1cdec
Property / Symbols used
 
Property / Symbols used: Q12692 / rank
 
Normal rank
Property / Symbols used: Q12692 / qualifier
 
test:

r 𝑟 {\displaystyle{\displaystyle r}}

r
Property / Symbols used: Q12692 / qualifier
 
xml-id: C33.S1.XMD3.m1cdec
Property / Symbols used
 
Property / Symbols used: Q12700 / rank
 
Normal rank
Property / Symbols used: Q12700 / qualifier
 
test:

𝖥 k ⁢ ( ℓ ; r ) subscript 𝖥 𝑘 ℓ 𝑟 {\displaystyle{\displaystyle\mathsf{F}_{k}(\ell;r)}}

\mathsf{F}_{k}(\ell;r)
Property / Symbols used: Q12700 / qualifier
 
xml-id: C33.S20.XMD1.m1adec

Latest revision as of 14:38, 2 January 2020

No description defined
Language Label Description Also known as
English
DLMF:33.20.E4
No description defined

    Statements

    test
    𝖥 k ⁢ ( ℓ ; r ) = ∑ p = 2 ⁢ k 3 ⁢ k ( 2 ⁢ r ) ( p + 1 ) / 2 ⁢ C k , p ⁢ J 2 ⁢ ℓ + 1 + p ⁡ ( 8 ⁢ r ) , subscript 𝖥 𝑘 ℓ 𝑟 superscript subscript 𝑝 2 𝑘 3 𝑘 superscript 2 𝑟 𝑝 1 2 subscript 𝐶 𝑘 𝑝 Bessel-J 2 ℓ 1 𝑝 8 𝑟 {\displaystyle{\displaystyle{\sf F}_{k}(\ell;r)=\sum_{p=2k}^{3k}(2r)^{(p+1)/2}% C_{k,p}J_{2\ell+1+p}\left(\sqrt{8r}\right),}}
    0 references
    DLMF id
    DLMF:33.20.E4
    0 references
    constraint
    r > 0 𝑟 0 {\displaystyle{\displaystyle r>0}}
    0 references
    Symbols used
    Bessel function of the first kind
    test
    J ν ⁡ ( z ) Bessel-J 𝜈 𝑧 {\displaystyle{\displaystyle J_{\NVar{\nu}}\left(\NVar{z}\right)}}
    xml-id
    C10.S2.E2.m2aadec
    0 references
    Q12669
    test
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C33.S1.XMD1.m1adec
    0 references
    Q12666
    test
    ℓ ℓ {\displaystyle{\displaystyle\ell}}
    xml-id
    C33.S1.XMD2.m1cdec
    0 references
    Q12692
    test
    r 𝑟 {\displaystyle{\displaystyle r}}
    xml-id
    C33.S1.XMD3.m1cdec
    0 references
    Q12700
    test
    𝖥 k ⁢ ( ℓ ; r ) subscript 𝖥 𝑘 ℓ 𝑟 {\displaystyle{\displaystyle\mathsf{F}_{k}(\ell;r)}}
    xml-id
    C33.S20.XMD1.m1adec
    0 references
     
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