DLMF:8.17.E22 (Q2663): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: beta function / rank
 
Normal rank
Property / Symbols used: beta function / qualifier
 
Defining formula:

B ⁡ ( a , b ) Euler-Beta 𝑎 𝑏 {\displaystyle{\displaystyle\mathrm{B}\left(\NVar{a},\NVar{b}\right)}}

\EulerBeta@{\NVar{a}}{\NVar{b}}
Property / Symbols used: beta function / qualifier
 
xml-id: C5.S12.E1.m2afdec
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.m2aodec
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.m1sdec
Property / Symbols used
 
Property / Symbols used: Q11369 / rank
 
Normal rank
Property / Symbols used: Q11369 / qualifier
 
Defining formula:

d m subscript 𝑑 𝑚 {\displaystyle{\displaystyle d_{m}}}

d_{m}
Property / Symbols used: Q11369 / qualifier
 
xml-id: C8.S17.XMD10.m1dec
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.m1rdec
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.m1sdec

Latest revision as of 14:05, 2 January 2020

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DLMF:8.17.E22
No description defined

    Statements

    Defining formula
    I x ⁡ ( a , b ) = x a ⁢ ( 1 - x ) b a ⁢ B ⁡ ( a , b ) ⁢ ( 1 1 + d 1 1 + d 2 1 + d 3 1 + ⁢ ⋯ ) , IncI 𝑥 𝑎 𝑏 superscript 𝑥 𝑎 superscript 1 𝑥 𝑏 𝑎 Euler-Beta 𝑎 𝑏 continued-fraction 1 1 continued-fraction subscript 𝑑 1 1 continued-fraction subscript 𝑑 2 1 continued-fraction subscript 𝑑 3 limit-from 1 ⋯ {\displaystyle{\displaystyle I_{x}\left(a,b\right)=\frac{x^{a}(1-x)^{b}}{a% \mathrm{B}\left(a,b\right)}\left(\cfrac{1}{1+\cfrac{d_{1}}{1+\cfrac{d_{2}}{1+% \cfrac{d_{3}}{1+}}}}\cdots\right),}}
    0 references
    DLMF id
    DLMF:8.17.E22
    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.m2afdec
    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.m2aodec
    0 references
    Q11360
    Defining formula
    a 𝑎 {\displaystyle{\displaystyle a}}
    xml-id
    C8.S17.XMD1.m1sdec
    0 references
    Q11369
    Defining formula
    d m subscript 𝑑 𝑚 {\displaystyle{\displaystyle d_{m}}}
    xml-id
    C8.S17.XMD10.m1dec
    0 references
    Q11361
    Defining formula
    b 𝑏 {\displaystyle{\displaystyle b}}
    xml-id
    C8.S17.XMD2.m1rdec
    0 references
    Q11362
    Defining formula
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C8.S17.XMD3.m1sdec
    0 references
     
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