DLMF:18.20.E9 (Q5851)

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DLMF:18.20.E9
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    Statements

    Defining formula
    p n ⁡ ( x ; a , b , a ¯ , b ¯ ) = i n ⁢ ( a + a ¯ ) n ⁢ ( a + b ¯ ) n n ! ⁢ F 2 3 ⁡ ( - n , n + 2 ⁢ ℜ ⁡ ( a + b ) - 1 , a + i ⁢ x a + a ¯ , a + b ¯ ; 1 ) . continuous-Hahn-polynomial-p 𝑛 𝑥 𝑎 𝑏 𝑎 𝑏 imaginary-unit 𝑛 Pochhammer 𝑎 𝑎 𝑛 Pochhammer 𝑎 𝑏 𝑛 𝑛 Gauss-hypergeometric-pFq 3 2 𝑛 𝑛 2 𝑎 𝑏 1 𝑎 imaginary-unit 𝑥 𝑎 𝑎 𝑎 𝑏 1 {\displaystyle{\displaystyle p_{n}\left(x;a,b,\overline{a},\overline{b}\right)% =\frac{{\mathrm{i}^{n}}{\left(a+\overline{a}\right)_{n}}{\left(a+\overline{b}% \right)_{n}}}{n!}\*{{}_{3}F_{2}}\left({-n,n+2\Re(a+b)-1,a+\mathrm{i}x\atop a+% \overline{a},a+\overline{b}};1\right).}}
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    DLMF id
    DLMF:18.20.E9
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