DLMF:10.23.E12 (Q3466): Difference between revisions

From testwiki
Jump to navigation Jump to search
← Older edit
imported>Admin
imported>Admin
Β 
(5 intermediate revisions by the same user not shown)
Property / constraint
Β 

| z | < | t | 𝑧 𝑑 {\displaystyle{\displaystyle|z|<|t|}}

|z|<|t|
Property / constraint: | z | < | t | 𝑧 𝑑 {\displaystyle{\displaystyle|z|<|t|}} / rank
Β 
Normal rank
Property / Symbols used
Β 
Property / Symbols used: Bessel function of the first kind / rank
Β 
Normal rank
Property / Symbols used: Bessel function of the first kind / qualifier
Β 
test:

J Ξ½ ⁑ ( 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
Β 
xml-id: C10.S2.E2.m2ahdec
Property / Symbols used
Β 
Property / Symbols used: Q11429 / rank
Β 
Normal rank
Property / Symbols used: Q11429 / qualifier
Β 
test:

n 𝑛 {\displaystyle{\displaystyle n}}

n
Property / Symbols used: Q11429 / qualifier
Β 
xml-id: C10.S1.XMD2.m1bdec
Property / Symbols used
Β 
Property / Symbols used: Q11428 / rank
Β 
Normal rank
Property / Symbols used: Q11428 / qualifier
Β 
test:

k π‘˜ {\displaystyle{\displaystyle k}}

k
Property / Symbols used: Q11428 / qualifier
Β 
xml-id: C10.S1.XMD3.m1jdec
Property / Symbols used
Β 
Property / Symbols used: Q11435 / rank
Β 
Normal rank
Property / Symbols used: Q11435 / qualifier
Β 
test:

x π‘₯ {\displaystyle{\displaystyle x}}

x
Property / Symbols used: Q11435 / qualifier
Β 
xml-id: C10.S1.XMD4.m1dec
Property / Symbols used
Β 
Property / Symbols used: Q11426 / rank
Β 
Normal rank
Property / Symbols used: Q11426 / qualifier
Β 
test:

z 𝑧 {\displaystyle{\displaystyle z}}

z
Property / Symbols used: Q11426 / qualifier
Β 
xml-id: C10.S1.XMD6.m1fdec

Latest revision as of 12:31, 2 January 2020

No description defined
Language Label Description Also known as
English
DLMF:10.23.E12
No description defined

    Statements

    test
    1 t - z = J 0 ⁑ ( z ) ⁒ O 0 ⁑ ( t ) + 2 ⁒ βˆ‘ k = 1 ∞ J k ⁑ ( z ) ⁒ O k ⁑ ( t ) , 1 𝑑 𝑧 Bessel-J 0 𝑧 Neumann-polynomial 0 𝑑 2 superscript subscript π‘˜ 1 Bessel-J π‘˜ 𝑧 Neumann-polynomial π‘˜ 𝑑 {\displaystyle{\displaystyle\frac{1}{t-z}=J_{0}\left(z\right)O_{0}\left(t% \right)+2\sum_{k=1}^{\infty}J_{k}\left(z\right)O_{k}\left(t\right),}}
    0 references
    DLMF id
    DLMF:10.23.E12
    0 references
    constraint
    | z | < | t | 𝑧 𝑑 {\displaystyle{\displaystyle|z|<|t|}}
    0 references
    Symbols used
    Bessel function of the first kind
    test
    J Ξ½ ⁑ ( z ) Bessel-J 𝜈 𝑧 {\displaystyle{\displaystyle J_{\NVar{\nu}}\left(\NVar{z}\right)}}
    xml-id
    C10.S2.E2.m2ahdec
    0 references
    Q11429
    test
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C10.S1.XMD2.m1bdec
    0 references
    Q11428
    test
    k π‘˜ {\displaystyle{\displaystyle k}}
    xml-id
    C10.S1.XMD3.m1jdec
    0 references
    Q11435
    test
    x π‘₯ {\displaystyle{\displaystyle x}}
    xml-id
    C10.S1.XMD4.m1dec
    0 references
    Q11426
    test
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C10.S1.XMD6.m1fdec
    0 references
     
      Retrieved from "https://lct.wmflabs.org/w/index.php?title=Item:Q3466&oldid=18347"