DLMF:28.25.E3 (Q8414)

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DLMF:28.25.E3
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    Statements

    Defining formula
    ( m + 1 ) ⁢ D m + 1 ± + ( ( m + 1 2 ) 2 ± ( m + 1 4 ) ⁢ 8 ⁢ i ⁢ h + 2 ⁢ h 2 - a ) ⁢ D m ± ± ( m - 1 2 ) ⁢ ( 8 ⁢ i ⁢ h ⁢ m ) ⁢ D m - 1 ± = 0 , plus-or-minus 𝑚 1 subscript superscript 𝐷 plus-or-minus 𝑚 1 plus-or-minus superscript 𝑚 1 2 2 𝑚 1 4 8 imaginary-unit ℎ 2 superscript ℎ 2 𝑎 subscript superscript 𝐷 plus-or-minus 𝑚 𝑚 1 2 8 imaginary-unit ℎ 𝑚 superscript subscript 𝐷 𝑚 1 plus-or-minus 0 {\displaystyle{\displaystyle(m+1)D^{\pm}_{m+1}+{\left((m+\tfrac{1}{2})^{2}\pm(% m+\tfrac{1}{4})8\mathrm{i}h+2h^{2}-a\right)D^{\pm}_{m}}\pm(m-\tfrac{1}{2})% \left(8\mathrm{i}hm\right)D_{m-1}^{\pm}=0,}}
    0 references
    DLMF id
    DLMF:28.25.E3
    0 references
    constraint
    m ≥ 0 𝑚 0 {\displaystyle{\displaystyle m\geq 0}}
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    Symbols used
    imaginary unit
    Defining formula
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    xml-id
    C1.S9.E1.m2aadec
    0 references
    Q12284
    Defining formula
    m 𝑚 {\displaystyle{\displaystyle m}}
    xml-id
    C28.S1.XMD1.m1bdec
    0 references
    Q12294
    Defining formula
    h ℎ {\displaystyle{\displaystyle h}}
    xml-id
    C28.S1.XMD11.m1adec
    0 references
    Q12273
    Defining formula
    a 𝑎 {\displaystyle{\displaystyle a}}
    xml-id
    C28.S1.XMD9.m1dec
    0 references
    Q12308
    Defining formula
    D m ± superscript subscript 𝐷 𝑚 plus-or-minus {\displaystyle{\displaystyle D_{m}^{\pm}}}
    xml-id
    C28.S25.XMD1.m1bdec
    0 references
     
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