DLMF:8.17.E21 (Q2662): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Q11362 / rank
 
Normal rank
Property / Symbols used: Q11362 / qualifier
 
Defining formula:

x 𝑥 {\displaystyle{\displaystyle x}}

x
Property / Symbols used: Q11362 / qualifier
 
xml-id: C8.S17.XMD3.m1rdec
Property / Symbols used
 
Property / Symbols used: Q11367 / rank
 
Normal rank
Property / Symbols used: Q11367 / qualifier
 
Defining formula:

x ′ superscript 𝑥 ′ {\displaystyle{\displaystyle x^{\prime}}}

x^{\prime}
Property / Symbols used: Q11367 / qualifier
 
xml-id: C8.S17.XMD9.m1gdec

Latest revision as of 14:05, 2 January 2020

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DLMF:8.17.E21
No description defined

    Statements

    Defining formula
    I x ⁡ ( a , b ) = I x ⁡ ( a , b + 1 ) - x a ⁢ ( x ′ ) b b ⁢ B ⁡ ( a , b ) . IncI 𝑥 𝑎 𝑏 IncI 𝑥 𝑎 𝑏 1 superscript 𝑥 𝑎 superscript superscript 𝑥 ′ 𝑏 𝑏 Euler-Beta 𝑎 𝑏 {\displaystyle{\displaystyle I_{x}\left(a,b\right)=I_{x}\left(a,b+1\right)-% \frac{x^{a}(x^{\prime})^{b}}{b\mathrm{B}\left(a,b\right)}.}}
    0 references
    DLMF id
    DLMF:8.17.E21
    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.m2aedec
    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.m2andec
    0 references
    Q11360
    Defining formula
    a 𝑎 {\displaystyle{\displaystyle a}}
    xml-id
    C8.S17.XMD1.m1rdec
    0 references
    Q11361
    Defining formula
    b 𝑏 {\displaystyle{\displaystyle b}}
    xml-id
    C8.S17.XMD2.m1qdec
    0 references
    Q11362
    Defining formula
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C8.S17.XMD3.m1rdec
    0 references
    Q11367
    Defining formula
    x ′ superscript 𝑥 ′ {\displaystyle{\displaystyle x^{\prime}}}
    xml-id
    C8.S17.XMD9.m1gdec
    0 references
     
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