DLMF:18.22.E28 (Q5899)

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DLMF:18.22.E28
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    Statements

    Defining formula
    δ x ( w ⁢ ( x ; a + 1 2 , b + 1 2 , a ¯ + 1 2 , b ¯ + 1 2 ) ⁢ p n ⁢ ( x ; a + 1 2 , b + 1 2 , a ¯ + 1 2 , b ¯ + 1 2 ) ) = - ( n + 1 ) ⁢ w ⁢ ( x ; a , b , a ¯ , b ¯ ) ⁢ p n + 1 ⁢ ( x ; a , b , a ¯ , b ¯ ) . central-difference 𝑥 𝑤 𝑥 𝑎 1 2 𝑏 1 2 𝑎 1 2 𝑏 1 2 subscript 𝑝 𝑛 𝑥 𝑎 1 2 𝑏 1 2 𝑎 1 2 𝑏 1 2 𝑛 1 𝑤 𝑥 𝑎 𝑏 𝑎 𝑏 subscript 𝑝 𝑛 1 𝑥 𝑎 𝑏 𝑎 𝑏 {\displaystyle{\displaystyle\delta_{x}\left(w(x;a+\tfrac{1}{2},b+\tfrac{1}{2},% \overline{a}+\tfrac{1}{2},\overline{b}+\tfrac{1}{2})p_{n}(x;a+\tfrac{1}{2},b+% \tfrac{1}{2},\overline{a}+\tfrac{1}{2},\overline{b}+\tfrac{1}{2})\right)=-(n+1% )w(x;a,b,\overline{a},\overline{b})p_{n+1}(x;a,b,\overline{a},\overline{b}).}}
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    DLMF id
    DLMF:18.22.E28
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