DLMF:10.29.E5 (Q3512): Difference between revisions

From DRMF
Jump to navigation Jump to search
← Older edit
‎Changed an Item: Add constraint
‎Changed an Item: Add constraint
 
(2 intermediate revisions by the same user not shown)
Property / Symbols used
 
Property / Symbols used: Q11428 / rank
 
Normal rank
Property / Symbols used: Q11428 / qualifier
 
Defining formula:

k 𝑘 {\displaystyle{\displaystyle k}}

k
Property / Symbols used: Q11428 / qualifier
 
xml-id: C10.S1.XMD3.m1adec
Property / Symbols used
 
Property / Symbols used: Q11426 / rank
 
Normal rank
Property / Symbols used: Q11426 / qualifier
 
Defining formula:

z 𝑧 {\displaystyle{\displaystyle z}}

z
Property / Symbols used: Q11426 / qualifier
 
xml-id: C10.S1.XMD6.m1ddec
Property / Symbols used
 
Property / Symbols used: Q11427 / rank
 
Normal rank
Property / Symbols used: Q11427 / qualifier
 
Defining formula:

ν 𝜈 {\displaystyle{\displaystyle\nu}}

\nu
Property / Symbols used: Q11427 / qualifier
 
xml-id: C10.S1.XMD7.m1cdec

Latest revision as of 13:38, 2 January 2020

No description defined
Language Label Description Also known as
English
DLMF:10.29.E5
No description defined

    Statements

    Defining formula
    𝒵 ν ( k ) ⁡ ( z ) = 1 2 k ⁢ ( 𝒵 ν - k ⁡ ( z ) + ( k 1 ) ⁢ 𝒵 ν - k + 2 ⁡ ( z ) + ( k 2 ) ⁢ 𝒵 ν - k + 4 ⁡ ( z ) + ⋯ + 𝒵 ν + k ⁡ ( z ) ) . modified-cylinder-function 𝜈 𝑘 𝑧 1 superscript 2 𝑘 modified-cylinder-function 𝜈 𝑘 𝑧 binomial 𝑘 1 modified-cylinder-function 𝜈 𝑘 2 𝑧 binomial 𝑘 2 modified-cylinder-function 𝜈 𝑘 4 𝑧 ⋯ modified-cylinder-function 𝜈 𝑘 𝑧 {\displaystyle{\displaystyle{\mathscr{Z}_{\nu}^{(k)}}\left(z\right)=\frac{1}{2% ^{k}}\left(\mathscr{Z}_{\nu-k}\left(z\right)+\genfrac{(}{)}{0.0pt}{}{k}{1}% \mathscr{Z}_{\nu-k+2}\left(z\right)+\genfrac{(}{)}{0.0pt}{}{k}{2}\mathscr{Z}_{% \nu-k+4}\left(z\right)+\cdots+\mathscr{Z}_{\nu+k}\left(z\right)\right).}}
    0 references
    DLMF id
    DLMF:10.29.E5
    0 references
    Symbols used
    Q10754
    Defining formula
    ( m n ) binomial 𝑚 𝑛 {\displaystyle{\displaystyle\genfrac{(}{)}{0.0pt}{}{\NVar{m}}{\NVar{n}}}}
    xml-id
    C1.S2.SS1.m1adec
    0 references
    Q11413
    Defining formula
    𝒵 ν ⁡ ( z ) modified-cylinder-function 𝜈 𝑧 {\displaystyle{\displaystyle\mathscr{Z}_{\NVar{\nu}}\left(\NVar{z}\right)}}
    xml-id
    C10.S25.Px2.p1.m3acdec
    0 references
    Q11428
    Defining formula
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C10.S1.XMD3.m1adec
    0 references
    Q11426
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C10.S1.XMD6.m1ddec
    0 references
    Q11427
    Defining formula
    ν 𝜈 {\displaystyle{\displaystyle\nu}}
    xml-id
    C10.S1.XMD7.m1cdec
    0 references
     
        Retrieved from "https://drmf-beta.wmflabs.org/index.php?title=Item:Q3512&oldid=38420"