DLMF:18.33.E3 (Q6009): Difference between revisions

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imported>Admin
 
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Property / Symbols used
 
Property / Symbols used: complex conjugate / rank
 
Normal rank
Property / Symbols used: complex conjugate / qualifier
 
test:

z ¯ 𝑧 {\displaystyle{\displaystyle\overline{\NVar{z}}}}

\conj{\NVar{z}}
Property / Symbols used: complex conjugate / qualifier
 
xml-id: C1.S9.E11.m2aadec
Property / Symbols used
 
Property / Symbols used: Q11750 / rank
 
Normal rank
Property / Symbols used: Q11750 / qualifier
 
test:

z 𝑧 {\displaystyle{\displaystyle z}}

z
Property / Symbols used: Q11750 / qualifier
 
xml-id: C18.S1.XMD2.m1bdec
Property / Symbols used
 
Property / Symbols used: Q11744 / rank
 
Normal rank
Property / Symbols used: Q11744 / qualifier
 
test:

{\displaystyle{\displaystyle\ell}}

\ell
Property / Symbols used: Q11744 / qualifier
 
xml-id: C18.S1.XMD4.m1adec
Property / Symbols used
 
Property / Symbols used: Q11726 / rank
 
Normal rank
Property / Symbols used: Q11726 / qualifier
 
test:

n 𝑛 {\displaystyle{\displaystyle n}}

n
Property / Symbols used: Q11726 / qualifier
 
xml-id: C18.S1.XMD6.m1bdec
Property / Symbols used
 
Property / Symbols used: Q11791 / rank
 
Normal rank
Property / Symbols used: Q11791 / qualifier
 
test:

ϕ n ( z ) subscript italic-ϕ 𝑛 𝑧 {\displaystyle{\displaystyle\phi_{n}(z)}}

\phi_{n}(z)
Property / Symbols used: Q11791 / qualifier
 
xml-id: C18.S33.XMD1.m1bdec

Latest revision as of 12:27, 2 January 2020

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DLMF:18.33.E3
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    Statements

    ϕ n * ( z ) = z n ϕ n ( z ¯ - 1 ) ¯ = κ n + = 1 n κ ¯ n , n - z , superscript subscript italic-ϕ 𝑛 𝑧 superscript 𝑧 𝑛 subscript italic-ϕ 𝑛 𝑧 1 subscript 𝜅 𝑛 superscript subscript 1 𝑛 subscript 𝜅 𝑛 𝑛 superscript 𝑧 {\displaystyle{\displaystyle\phi_{n}^{*}(z)=z^{n}\overline{\phi_{n}({\overline% {z}^{-1}})}={\kappa_{n}}+\sum_{\ell=1}^{n}\overline{\kappa}_{n,n-\ell}z^{\ell}% ,}}
    0 references
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    z ¯ 𝑧 {\displaystyle{\displaystyle\overline{\NVar{z}}}}
    C1.S9.E11.m2aadec
    0 references
    z 𝑧 {\displaystyle{\displaystyle z}}
    C18.S1.XMD2.m1bdec
    0 references
    {\displaystyle{\displaystyle\ell}}
    C18.S1.XMD4.m1adec
    0 references
    n 𝑛 {\displaystyle{\displaystyle n}}
    C18.S1.XMD6.m1bdec
    0 references
    ϕ n ( z ) subscript italic-ϕ 𝑛 𝑧 {\displaystyle{\displaystyle\phi_{n}(z)}}
    C18.S33.XMD1.m1bdec
    0 references