DLMF:8.17.E19 (Q2660): Difference between revisions

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‎Changed an Item: Add constraint
‎Changed an Item: Add constraint
Property / Symbols used
 
Property / Symbols used: incomplete beta function / rank
 
Normal rank
Property / Symbols used: incomplete beta function / qualifier
 
Defining formula:

I x ⁡ ( a , b ) IncI 𝑥 𝑎 𝑏 {\displaystyle{\displaystyle I_{\NVar{x}}\left(\NVar{a},\NVar{b}\right)}}

\normincBetaI{\NVar{x}}@{\NVar{a}}{\NVar{b}}
Property / Symbols used: incomplete beta function / qualifier
 
xml-id: C8.S17.E2.m2aldec

Revision as of 14:04, 2 January 2020

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DLMF:8.17.E19
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    Statements

    Defining formula
    I x ⁡ ( a , b ) = I x ⁡ ( a - 1 , b + 1 ) - x a - 1 ⁢ ( x ′ ) b b ⁢ B ⁡ ( a , b ) , IncI 𝑥 𝑎 𝑏 IncI 𝑥 𝑎 1 𝑏 1 superscript 𝑥 𝑎 1 superscript superscript 𝑥 ′ 𝑏 𝑏 Euler-Beta 𝑎 𝑏 {\displaystyle{\displaystyle I_{x}\left(a,b\right)=I_{x}\left(a-1,b+1\right)-% \frac{x^{a-1}(x^{\prime})^{b}}{b\mathrm{B}\left(a,b\right)},}}
    0 references
    DLMF id
    DLMF:8.17.E19
    0 references
    Symbols used
    beta function
    Defining formula
    B ⁡ ( a , b ) Euler-Beta 𝑎 𝑏 {\displaystyle{\displaystyle\mathrm{B}\left(\NVar{a},\NVar{b}\right)}}
    xml-id
    C5.S12.E1.m2acdec
    0 references
    incomplete beta function
    Defining formula
    I x ⁡ ( a , b ) IncI 𝑥 𝑎 𝑏 {\displaystyle{\displaystyle I_{\NVar{x}}\left(\NVar{a},\NVar{b}\right)}}
    xml-id
    C8.S17.E2.m2aldec
    0 references
     
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