DLMF:10.44.E3 (Q3651): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Q11413 / rank
 
Normal rank
Property / Symbols used: Q11413 / qualifier
 
test:

𝒵 ν ( z ) modified-cylinder-function 𝜈 𝑧 {\displaystyle{\displaystyle\mathscr{Z}_{\NVar{\nu}}\left(\NVar{z}\right)}}

\modcylinder{\NVar{\nu}}@{\NVar{z}}
Property / Symbols used: Q11413 / qualifier
 
xml-id: C10.S25.Px2.p1.m3aadec
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.m1bdec
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.m1bdec

Latest revision as of 13:05, 2 January 2020

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DLMF:10.44.E3
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    Statements

    𝒵 ν ( u ± v ) = k = - ( ± 1 ) k 𝒵 ν + k ( u ) I k ( v ) , modified-cylinder-function 𝜈 plus-or-minus 𝑢 𝑣 superscript subscript 𝑘 superscript plus-or-minus 1 𝑘 modified-cylinder-function 𝜈 𝑘 𝑢 modified-Bessel-first-kind 𝑘 𝑣 {\displaystyle{\displaystyle\mathscr{Z}_{\nu}\left(u\pm v\right)=\sum_{k=-% \infty}^{\infty}(\pm 1)^{k}\mathscr{Z}_{\nu+k}\left(u\right)I_{k}\left(v\right% ),}}
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    | v | < | u | 𝑣 𝑢 {\displaystyle{\displaystyle|v|<|u|}}
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    I ν ( z ) modified-Bessel-first-kind 𝜈 𝑧 {\displaystyle{\displaystyle I_{\NVar{\nu}}\left(\NVar{z}\right)}}
    C10.S25.E2.m2aadec
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    𝒵 ν ( z ) modified-cylinder-function 𝜈 𝑧 {\displaystyle{\displaystyle\mathscr{Z}_{\NVar{\nu}}\left(\NVar{z}\right)}}
    C10.S25.Px2.p1.m3aadec
    0 references
    k 𝑘 {\displaystyle{\displaystyle k}}
    C10.S1.XMD3.m1bdec
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    ν 𝜈 {\displaystyle{\displaystyle\nu}}
    C10.S1.XMD7.m1bdec
    0 references