DLMF:30.11.E7 (Q8902)

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DLMF:30.11.E7
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    Statements

    Defining formula
    𝒲 ⁡ { S n m ⁢ ( 1 ) ⁡ ( z , γ ) , S n m ⁢ ( 2 ) ⁡ ( z , γ ) } = 1 γ ⁢ ( z 2 - 1 ) . Wronskian radial-spheroidal-wave-S 𝑚 1 𝑛 𝑧 𝛾 radial-spheroidal-wave-S 𝑚 2 𝑛 𝑧 𝛾 1 𝛾 superscript 𝑧 2 1 {\displaystyle{\displaystyle\mathscr{W}\left\{S^{m(1)}_{n}\left(z,\gamma\right% ),S^{m(2)}_{n}\left(z,\gamma\right)\right\}=\frac{1}{\gamma(z^{2}-1)}.}}
    0 references
    DLMF id
    DLMF:30.11.E7
    0 references
    Symbols used
    Q10865
    Defining formula
    𝒲 Wronskian {\displaystyle{\displaystyle\mathscr{W}}}
    xml-id
    C1.S13.Px2.p1.m3adec
    0 references
    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.m2agdec
    0 references
    Q12401
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C30.S1.XMD1.m1ddec
    0 references
    Q12408
    Defining formula
    m 𝑚 {\displaystyle{\displaystyle m}}
    xml-id
    C30.S1.XMD4.m1ddec
    0 references
    Q12409
    Defining formula
    n ≥ m 𝑛 𝑚 {\displaystyle{\displaystyle n\geq m}}
    xml-id
    C30.S1.XMD5.m1hdec
    0 references
     
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