DLMF:30.14.E8 (Q8941)

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DLMF:30.14.E8
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    Statements

    Defining formula
    w 1 ⁢ ( ξ ) = a 1 ⁢ S n m ⁢ ( 1 ) ⁡ ( i ⁢ ξ , γ ) + b 1 ⁢ S n m ⁢ ( 2 ) ⁡ ( i ⁢ ξ , γ ) . subscript 𝑤 1 𝜉 subscript 𝑎 1 radial-spheroidal-wave-S 𝑚 1 𝑛 𝑖 𝜉 𝛾 subscript 𝑏 1 radial-spheroidal-wave-S 𝑚 2 𝑛 𝑖 𝜉 𝛾 {\displaystyle{\displaystyle w_{1}(\xi)=a_{1}S^{m(1)}_{n}\left(i\xi,\gamma% \right)+b_{1}S^{m(2)}_{n}\left(i\xi,\gamma\right).}}
    0 references
    DLMF id
    DLMF:30.14.E8
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    Symbols used
    imaginary unit
    Defining formula
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    xml-id
    C1.S9.E1.m2adec
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    radial spheroidal wave function
    Defining formula
    S n m ⁢ ( j ) ⁡ ( z , γ ) radial-spheroidal-wave-S 𝑚 𝑗 𝑛 𝑧 𝛾 {\displaystyle{\displaystyle S^{\NVar{m}(\NVar{j})}_{\NVar{n}}\left(\NVar{z},% \NVar{\gamma}\right)}}
    xml-id
    C30.S11.E3.m2adec
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    Q12408
    Defining formula
    m 𝑚 {\displaystyle{\displaystyle m}}
    xml-id
    C30.S1.XMD4.m1dec
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    Q12409
    Defining formula
    n ≥ m 𝑛 𝑚 {\displaystyle{\displaystyle n\geq m}}
    xml-id
    C30.S1.XMD5.m1dec
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    Q12443
    Defining formula
    b j subscript 𝑏 𝑗 {\displaystyle{\displaystyle b_{j}}}
    xml-id
    C30.S13.XMD10.m1dec
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    Q12444
    Defining formula
    a j subscript 𝑎 𝑗 {\displaystyle{\displaystyle a_{j}}}
    xml-id
    C30.S13.XMD9.m1dec
    0 references
    Q12445
    Defining formula
    ξ 𝜉 {\displaystyle{\displaystyle\xi}}
    xml-id
    C30.S14.XMD1.m1gdec
    0 references
    Q12449
    Defining formula
    w j subscript 𝑤 𝑗 {\displaystyle{\displaystyle w_{j}}}
    xml-id
    C30.S14.XMD5.m1adec
    0 references
     
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