DLMF:8.17.E18 (Q2659): Difference between revisions

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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.m2akdec
Property / Symbols used
 
Property / Symbols used: Q11360 / rank
 
Normal rank
Property / Symbols used: Q11360 / qualifier
 
Defining formula:

a 𝑎 {\displaystyle{\displaystyle a}}

a
Property / Symbols used: Q11360 / qualifier
 
xml-id: C8.S17.XMD1.m1odec
Property / Symbols used
 
Property / Symbols used: Q11361 / rank
 
Normal rank
Property / Symbols used: Q11361 / qualifier
 
Defining formula:

b 𝑏 {\displaystyle{\displaystyle b}}

b
Property / Symbols used: Q11361 / qualifier
 
xml-id: C8.S17.XMD2.m1ndec
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.m1odec
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.m1ddec

Latest revision as of 14:04, 2 January 2020

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DLMF:8.17.E18
No description defined

    Statements

    Defining formula
    I x ⁡ ( a , b ) = I x ⁡ ( a + 1 , b - 1 ) + x a ⁢ ( x ′ ) b - 1 a ⁢ B ⁡ ( a , b ) , IncI 𝑥 𝑎 𝑏 IncI 𝑥 𝑎 1 𝑏 1 superscript 𝑥 𝑎 superscript superscript 𝑥 ′ 𝑏 1 𝑎 Euler-Beta 𝑎 𝑏 {\displaystyle{\displaystyle I_{x}\left(a,b\right)=I_{x}\left(a+1,b-1\right)+% \frac{x^{a}(x^{\prime})^{b-1}}{a\mathrm{B}\left(a,b\right)},}}
    0 references
    DLMF id
    DLMF:8.17.E18
    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.m2abdec
    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.m2akdec
    0 references
    Q11360
    Defining formula
    a 𝑎 {\displaystyle{\displaystyle a}}
    xml-id
    C8.S17.XMD1.m1odec
    0 references
    Q11361
    Defining formula
    b 𝑏 {\displaystyle{\displaystyle b}}
    xml-id
    C8.S17.XMD2.m1ndec
    0 references
    Q11362
    Defining formula
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C8.S17.XMD3.m1odec
    0 references
    Q11367
    Defining formula
    x ′ superscript 𝑥 ′ {\displaystyle{\displaystyle x^{\prime}}}
    xml-id
    C8.S17.XMD9.m1ddec
    0 references
     
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