DLMF:18.22.E28 (Q5899): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Q11727 / rank
 
Normal rank
Property / Symbols used: Q11727 / qualifier
 
Defining formula:

x 𝑥 {\displaystyle{\displaystyle x}}

x
Property / Symbols used: Q11727 / qualifier
 
xml-id: C18.S2.XMD3.m1aadec

Latest revision as of 01:38, 2 January 2020

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DLMF:18.22.E28
No description defined

    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}).}}
    0 references
    DLMF id
    DLMF:18.22.E28
    0 references
    Symbols used
    Q11767
    Defining formula
    δ x central-difference 𝑥 {\displaystyle{\displaystyle\delta_{\NVar{x}}}}
    xml-id
    C18.S1.EGx3.m1aadec
    0 references
    complex conjugate
    Defining formula
    z ¯ 𝑧 {\displaystyle{\displaystyle\overline{\NVar{z}}}}
    xml-id
    C1.S9.E11.m2aedec
    0 references
    Q11729
    Defining formula
    w ⁢ ( x ) 𝑤 𝑥 {\displaystyle{\displaystyle w(x)}}
    xml-id
    C18.S1.XMD10.m1dec
    0 references
    Q11726
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C18.S1.XMD6.m1zdec
    0 references
    Q11731
    Defining formula
    p n ⁢ ( x ) subscript 𝑝 𝑛 𝑥 {\displaystyle{\displaystyle p_{n}(x)}}
    xml-id
    C18.S1.XMD9.m1mdec
    0 references
    Q11727
    Defining formula
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C18.S2.XMD3.m1aadec
    0 references
     
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