DLMF:10.23.E4 (Q3456): Difference between revisions

From testwiki
Jump to navigation Jump to search
imported>Admin
imported>Admin
 
(3 intermediate revisions by the same user not shown)
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.m2abdec
Property / Symbols used
 
Property / Symbols used: Q11429 / rank
 
Normal rank
Property / Symbols used: Q11429 / qualifier
 
test:

n 𝑛 {\displaystyle{\displaystyle n}}

n
Property / Symbols used: Q11429 / qualifier
 
xml-id: C10.S1.XMD2.m1dec
Property / Symbols used
 
Property / Symbols used: Q11428 / rank
 
Normal rank
Property / Symbols used: Q11428 / qualifier
 
test:

k 𝑘 {\displaystyle{\displaystyle k}}

k
Property / Symbols used: Q11428 / qualifier
 
xml-id: C10.S1.XMD3.m1cdec
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.m1bdec

Latest revision as of 13:29, 2 January 2020

No description defined
Language Label Description Also known as
English
DLMF:10.23.E4
No description defined

    Statements

    k = 0 2 n ( - 1 ) k J k ( z ) J 2 n - k ( z ) + 2 k = 1 J k ( z ) J 2 n + k ( z ) = 0 , superscript subscript 𝑘 0 2 𝑛 superscript 1 𝑘 Bessel-J 𝑘 𝑧 Bessel-J 2 𝑛 𝑘 𝑧 2 superscript subscript 𝑘 1 Bessel-J 𝑘 𝑧 Bessel-J 2 𝑛 𝑘 𝑧 0 {\displaystyle{\displaystyle\sum_{k=0}^{2n}(-1)^{k}J_{k}\left(z\right)J_{2n-k}% \left(z\right)\\ +2\sum_{k=1}^{\infty}J_{k}\left(z\right)J_{2n+k}\left(z\right)=0,}}
    0 references
    0 references
    n 1 𝑛 1 {\displaystyle{\displaystyle n\geq 1}}
    0 references
    J ν ( z ) Bessel-J 𝜈 𝑧 {\displaystyle{\displaystyle J_{\NVar{\nu}}\left(\NVar{z}\right)}}
    C10.S2.E2.m2abdec
    0 references
    n 𝑛 {\displaystyle{\displaystyle n}}
    C10.S1.XMD2.m1dec
    0 references
    k 𝑘 {\displaystyle{\displaystyle k}}
    C10.S1.XMD3.m1cdec
    0 references
    z 𝑧 {\displaystyle{\displaystyle z}}
    C10.S1.XMD6.m1bdec
    0 references