DLMF:32.2.E13 (Q9167): Difference between revisions

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‎Changed an Item: Add constraint
Property / Symbols used
 
Property / Symbols used: Q12529 / rank
 
Normal rank
Property / Symbols used: Q12529 / qualifier
 
Defining formula:

I 𝐼 {\displaystyle{\displaystyle I}}

I
Property / Symbols used: Q12529 / qualifier
 
xml-id: C32.S2.XMD12.m1dec

Revision as of 13:49, 2 January 2020

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DLMF:32.2.E13
No description defined

    Statements

    Defining formula
    z ⁢ ( 1 - z ) ⁢ I ⁢ ( ∫ ∞ w d t t ⁢ ( t - 1 ) ⁢ ( t - z ) ) = w ⁢ ( w - 1 ) ⁢ ( w - z ) ⁢ ( α + β ⁢ z w 2 + γ ⁢ ( z - 1 ) ( w - 1 ) 2 + ( δ - 1 2 ) ⁢ z ⁢ ( z - 1 ) ( w - z ) 2 ) , 𝑧 1 𝑧 𝐼 superscript subscript 𝑤 𝑡 𝑡 𝑡 1 𝑡 𝑧 𝑤 𝑤 1 𝑤 𝑧 𝛼 𝛽 𝑧 superscript 𝑤 2 𝛾 𝑧 1 superscript 𝑤 1 2 𝛿 1 2 𝑧 𝑧 1 superscript 𝑤 𝑧 2 {\displaystyle{\displaystyle z(1-z)I\left(\int_{\infty}^{w}\frac{\mathrm{d}t}{% \sqrt{t(t-1)(t-z)}}\right)=\sqrt{w(w-1)(w-z)}\*\left(\alpha+\frac{\beta z}{w^{% 2}}+\frac{\gamma(z-1)}{(w-1)^{2}}+(\delta-\tfrac{1}{2})\frac{z(z-1)}{(w-z)^{2}% }\right),}}
    0 references
    DLMF id
    DLMF:32.2.E13
    0 references
    Symbols used
    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
    Q12523
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C32.S1.XMD4.m1idec
    0 references
    Q12524
    Defining formula
    α 𝛼 {\displaystyle{\displaystyle\alpha}}
    xml-id
    C32.S2.XMD1.m1hdec
    0 references
    Q12529
    Defining formula
    I 𝐼 {\displaystyle{\displaystyle I}}
    xml-id
    C32.S2.XMD12.m1dec
    0 references
     
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