DLMF:12.10.E33 (Q4197): Difference between revisions

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‎Changed an Item: Add constraint
‎Changed an Item: Add constraint
 
Property / Symbols used
 
Property / Symbols used: DLMF:12.10.E32 / rank
 
Normal rank
Property / Symbols used: DLMF:12.10.E32 / qualifier
 
Defining formula:

τ 𝜏 {\displaystyle{\displaystyle\tau}}

\tau
Property / Symbols used: DLMF:12.10.E32 / qualifier
 
xml-id: C12.S10.XMD19.m1bdec

Latest revision as of 15:21, 2 January 2020

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DLMF:12.10.E33
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    Statements

    Defining formula
    𝖠 s + 1 ⁢ ( τ ) = - 4 ⁢ τ 2 ⁢ ( τ + 1 ) 2 ⁢ d d τ ⁡ 𝖠 s ⁢ ( τ ) - 1 4 ⁢ ∫ 0 τ ( 20 ⁢ u 2 + 20 ⁢ u + 3 ) ⁢ 𝖠 s ⁢ ( u ) ⁢ d u , subscript 𝖠 𝑠 1 𝜏 4 superscript 𝜏 2 superscript 𝜏 1 2 derivative 𝜏 subscript 𝖠 𝑠 𝜏 1 4 superscript subscript 0 𝜏 20 superscript 𝑢 2 20 𝑢 3 subscript 𝖠 𝑠 𝑢 𝑢 {\displaystyle{\displaystyle\mathsf{A}_{s+1}(\tau)=-4\tau^{2}(\tau+1)^{2}\frac% {\mathrm{d}}{\mathrm{d}\tau}\mathsf{A}_{s}(\tau)-\frac{1}{4}\int_{0}^{\tau}% \left(20u^{2}+20u+3\right)\mathsf{A}_{s}(u)\mathrm{d}u,}}
    0 references
    DLMF id
    DLMF:12.10.E33
    0 references
    constraint
    s = 0 , 1 , 2 , … 𝑠 0 1 2 … {\displaystyle{\displaystyle s=0,1,2,\dots}}
    0 references
    Symbols used
    derivative of $$f$$ with respect to $$x$$
    Defining formula
    d f d x derivative 𝑓 𝑥 {\displaystyle{\displaystyle\frac{\mathrm{d}\NVar{f}}{\mathrm{d}\NVar{x}}}}
    xml-id
    C1.S4.E4.m2aadec
    0 references
    Q10770
    Defining formula
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1adec
    0 references
    Q10771
    Defining formula
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3adec
    0 references
    Q11526
    Defining formula
    s 𝑠 {\displaystyle{\displaystyle s}}
    xml-id
    C12.S1.XMD5.m1wdec
    0 references
    DLMF:12.10.E32
    Defining formula
    τ 𝜏 {\displaystyle{\displaystyle\tau}}
    xml-id
    C12.S10.XMD19.m1bdec
    0 references
     
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