DLMF:18.22.E5 (Q5872): Difference between revisions

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Changed an Item: Add constraint
Changed an Item: Add constraint
Property / Symbols used
 
Property / Symbols used: Q11726 / rank
 
Normal rank
Property / Symbols used: Q11726 / qualifier
 
Defining formula:

n 𝑛 {\displaystyle{\displaystyle n}}

n
Property / Symbols used: Q11726 / qualifier
 
xml-id: C18.S1.XMD6.m1edec

Revision as of 01:34, 2 January 2020

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DLMF:18.22.E5
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    Statements

    ( a + i x ) q n ( x ) = A ~ n q n + 1 ( x ) - ( A ~ n + C ~ n ) q n ( x ) + C ~ n q n - 1 ( x ) , 𝑎 imaginary-unit 𝑥 subscript 𝑞 𝑛 𝑥 subscript ~ 𝐴 𝑛 subscript 𝑞 𝑛 1 𝑥 subscript ~ 𝐴 𝑛 subscript ~ 𝐶 𝑛 subscript 𝑞 𝑛 𝑥 subscript ~ 𝐶 𝑛 subscript 𝑞 𝑛 1 𝑥 {\displaystyle{\displaystyle(a+\mathrm{i}x)q_{n}(x)=\tilde{A}_{n}q_{n+1}(x)-% \bigl{(}\tilde{A}_{n}+\tilde{C}_{n}\bigr{)}q_{n}(x)+\tilde{C}_{n}q_{n-1}(x),}}
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    DLMF:18.22.E5
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    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    C1.S9.E1.m2aadec
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    n 𝑛 {\displaystyle{\displaystyle n}}
    C18.S1.XMD6.m1edec
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