DLMF:2.9.E7 (Q980): Difference between revisions

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‎Changed an Item: Add constraint
‎Changed an Item: Add constraint
Property / Symbols used
 
Property / Symbols used: Q11100 / rank
 
Normal rank
Property / Symbols used: Q11100 / qualifier
 
Defining formula:

f s subscript 𝑓 𝑠 {\displaystyle{\displaystyle f_{s}}}

f_{s}
Property / Symbols used: Q11100 / qualifier
 
xml-id: C2.S9.XMD5.m1cdec

Revision as of 17:31, 1 January 2020

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DLMF:2.9.E7
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    Statements

    Defining formula
    ρ j ⁢ ( f 0 + 2 ⁢ ρ j ) ⁢ s ⁢ a s , j = ∑ r = 1 s ( ρ j 2 ⁢ 2 r + 1 ⁢ ( α j + r - s r + 1 ) + ρ j ⁢ ∑ q = 0 r + 1 ( α j + r - s r + 1 - q ) ⁢ f q + g r + 1 ) ⁢ a s - r , j , subscript 𝜌 𝑗 subscript 𝑓 0 2 subscript 𝜌 𝑗 𝑠 subscript 𝑎 𝑠 𝑗 superscript subscript 𝑟 1 𝑠 superscript subscript 𝜌 𝑗 2 superscript 2 𝑟 1 binomial subscript 𝛼 𝑗 𝑟 𝑠 𝑟 1 subscript 𝜌 𝑗 superscript subscript 𝑞 0 𝑟 1 binomial subscript 𝛼 𝑗 𝑟 𝑠 𝑟 1 𝑞 subscript 𝑓 𝑞 subscript 𝑔 𝑟 1 subscript 𝑎 𝑠 𝑟 𝑗 {\displaystyle{\displaystyle\rho_{j}(f_{0}+2\rho_{j})sa_{s,j}=\sum_{r=1}^{s}% \left(\rho_{j}^{2}2^{r+1}\genfrac{(}{)}{0.0pt}{}{\alpha_{j}+r-s}{r+1}+\rho_{j}% \sum_{q=0}^{r+1}\genfrac{(}{)}{0.0pt}{}{\alpha_{j}+r-s}{r+1-q}f_{q}+g_{r+1}% \right)a_{s-r,j},}}
    0 references
    DLMF id
    DLMF:2.9.E7
    0 references
    Symbols used
    Q10754
    Defining formula
    ( m n ) binomial 𝑚 𝑛 {\displaystyle{\displaystyle\genfrac{(}{)}{0.0pt}{}{\NVar{m}}{\NVar{n}}}}
    xml-id
    C1.S2.SS1.m1adec
    0 references
    Q11100
    Defining formula
    f s subscript 𝑓 𝑠 {\displaystyle{\displaystyle f_{s}}}
    xml-id
    C2.S9.XMD5.m1cdec
    0 references
     
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