DLMF:10.23.E9 (Q3463)

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DLMF:10.23.E9
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    test
    e i ⁢ v ⁢ cos ⁡ α = Γ ⁡ ( ν ) ( 1 2 ⁢ v ) ν ⁢ ∑ k = 0 ∞ ( ν + k ) ⁢ i k ⁢ J ν + k ⁡ ( v ) ⁢ C k ( ν ) ⁡ ( cos ⁡ α ) , superscript 𝑒 𝑖 𝑣 𝛼 Euler-Gamma 𝜈 superscript 1 2 𝑣 𝜈 superscript subscript 𝑘 0 𝜈 𝑘 superscript 𝑖 𝑘 Bessel-J 𝜈 𝑘 𝑣 ultraspherical-Gegenbauer-polynomial 𝜈 𝑘 𝛼 {\displaystyle{\displaystyle e^{iv\cos\alpha}=\frac{\Gamma\left(\nu\right)}{(% \tfrac{1}{2}v)^{\nu}}\*\sum_{k=0}^{\infty}(\nu+k)i^{k}J_{\nu+k}\left(v\right)C% ^{(\nu)}_{k}\left(\cos\alpha\right),}}
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    DLMF:10.23.E9
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