DLMF:30.8.E2 (Q8866)

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DLMF:30.8.E2
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    Statements

    Defining formula
    a n , k m ⁢ ( γ 2 ) = ( - 1 ) k ⁢ ( n + 2 ⁢ k + 1 2 ) ⁢ ( n - m + 2 ⁢ k ) ! ( n + m + 2 ⁢ k ) ! ⁢ ∫ - 1 1 𝖯𝗌 n m ⁡ ( x , γ 2 ) ⁢ 𝖯 n + 2 ⁢ k m ⁡ ( x ) ⁢ d x . subscript superscript 𝑎 𝑚 𝑛 𝑘 superscript 𝛾 2 superscript 1 𝑘 𝑛 2 𝑘 1 2 𝑛 𝑚 2 𝑘 𝑛 𝑚 2 𝑘 superscript subscript 1 1 spheroidal-wave-on-cut-Ps 𝑚 𝑛 𝑥 superscript 𝛾 2 Ferrers-Legendre-P-first-kind 𝑚 𝑛 2 𝑘 𝑥 𝑥 {\displaystyle{\displaystyle a^{m}_{n,k}(\gamma^{2})=(-1)^{k}\left(n+2k+\tfrac% {1}{2}\right)\frac{(n-m+2k)!}{(n+m+2k)!}\*\int_{-1}^{1}\mathsf{Ps}^{m}_{n}% \left(x,\gamma^{2}\right)\mathsf{P}^{m}_{n+2k}\left(x\right)\mathrm{d}x.}}
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    DLMF id
    DLMF:30.8.E2
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