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

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Changed an Item: Add constraint
Changed an Item: Add constraint
 
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
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    Statements

    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:18.22.E28
    0 references
    δ x central-difference 𝑥 {\displaystyle{\displaystyle\delta_{\NVar{x}}}}
    C18.S1.EGx3.m1aadec
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    z ¯ 𝑧 {\displaystyle{\displaystyle\overline{\NVar{z}}}}
    C1.S9.E11.m2aedec
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    w ( x ) 𝑤 𝑥 {\displaystyle{\displaystyle w(x)}}
    C18.S1.XMD10.m1dec
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    n 𝑛 {\displaystyle{\displaystyle n}}
    C18.S1.XMD6.m1zdec
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    p n ( x ) subscript 𝑝 𝑛 𝑥 {\displaystyle{\displaystyle p_{n}(x)}}
    C18.S1.XMD9.m1mdec
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    x 𝑥 {\displaystyle{\displaystyle x}}
    C18.S2.XMD3.m1aadec
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