DLMF:30.11.E9 (Q8904): Difference between revisions

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Changed an Item: Add constraint
Changed an Item: Add constraint
 
Property / Symbols used
 
Property / Symbols used: Q12404 / rank
 
Normal rank
Property / Symbols used: Q12404 / qualifier
 
Defining formula:

γ 2 superscript 𝛾 2 {\displaystyle{\displaystyle\gamma^{2}}}

\gamma^{2}
Property / Symbols used: Q12404 / qualifier
 
xml-id: C30.S2.XMD3.m1fdec

Latest revision as of 01:49, 2 January 2020

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DLMF:30.11.E9
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    Statements

    S n m ( 2 ) ( z , γ ) = ( n - m ) ! ( n + m ) ! ( - 1 ) m + 1 𝑄𝑠 n m ( z , γ 2 ) γ K n m ( γ ) A n m ( γ 2 ) A n - m ( γ 2 ) , radial-spheroidal-wave-S 𝑚 2 𝑛 𝑧 𝛾 𝑛 𝑚 𝑛 𝑚 superscript 1 𝑚 1 spheroidal-wave-Qs 𝑚 𝑛 𝑧 superscript 𝛾 2 𝛾 superscript subscript 𝐾 𝑛 𝑚 𝛾 superscript subscript 𝐴 𝑛 𝑚 superscript 𝛾 2 superscript subscript 𝐴 𝑛 𝑚 superscript 𝛾 2 {\displaystyle{\displaystyle S^{m(2)}_{n}\left(z,\gamma\right)=\frac{(n-m)!}{(% n+m)!}\frac{(-1)^{m+1}\mathit{Qs}^{m}_{n}\left(z,\gamma^{2}\right)}{\gamma K_{% n}^{m}(\gamma)A_{n}^{m}(\gamma^{2})A_{n}^{-m}(\gamma^{2})},}}
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    DLMF:30.11.E9
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    ! {\displaystyle{\displaystyle!}}
    introduction.Sx4.p1.t1.r15.m5adec
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    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)}}
    C30.S11.E3.m2aidec
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    𝑄𝑠 n m ( z , γ 2 ) spheroidal-wave-Qs 𝑚 𝑛 𝑧 superscript 𝛾 2 {\displaystyle{\displaystyle\mathit{Qs}^{\NVar{m}}_{\NVar{n}}\left(\NVar{z},% \NVar{\gamma^{2}}\right)}}
    C30.S6.p1.m2adec
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    z 𝑧 {\displaystyle{\displaystyle z}}
    C30.S1.XMD1.m1fdec
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    m 𝑚 {\displaystyle{\displaystyle m}}
    C30.S1.XMD4.m1fdec
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    n m 𝑛 𝑚 {\displaystyle{\displaystyle n\geq m}}
    C30.S1.XMD5.m1jdec
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    A n m ( γ 2 ) superscript subscript 𝐴 𝑛 𝑚 superscript 𝛾 2 {\displaystyle{\displaystyle A_{n}^{m}(\gamma^{2})}}
    C30.S11.XMD5.m1bdec
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    K n m ( γ ) superscript subscript 𝐾 𝑛 𝑚 𝛾 {\displaystyle{\displaystyle K_{n}^{m}(\gamma)}}
    C30.S11.XMD6.m1adec
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    γ 2 superscript 𝛾 2 {\displaystyle{\displaystyle\gamma^{2}}}
    C30.S2.XMD3.m1fdec
    0 references