DLMF:8.17.E7 (Q2647): Difference between revisions

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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.m1ddec
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.m1edec

Latest revision as of 14:02, 2 January 2020

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DLMF:8.17.E7
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    Statements

    Defining formula
    B x ⁡ ( a , b ) = x a a ⁢ F ⁡ ( a , 1 - b ; a + 1 ; x ) , incomplete-Beta 𝑥 𝑎 𝑏 superscript 𝑥 𝑎 𝑎 Gauss-hypergeometric-F 𝑎 1 𝑏 𝑎 1 𝑥 {\displaystyle{\displaystyle\mathrm{B}_{x}\left(a,b\right)=\frac{x^{a}}{a}F% \left(a,1-b;a+1;x\right),}}
    0 references
    DLMF id
    DLMF:8.17.E7
    0 references
    Symbols used
    $$={{}_{2}F_{1}}\left(\NVar{a},\NVar{b};\NVar{c};\NVar{z}\right)$$ Gauss’ hypergeometric function
    Defining formula
    F ⁡ ( a , b ; c ; z ) Gauss-hypergeometric-F 𝑎 𝑏 𝑐 𝑧 {\displaystyle{\displaystyle F\left(\NVar{a},\NVar{b};\NVar{c};\NVar{z}\right)}}
    xml-id
    C15.S2.E1.m2adec
    0 references
    incomplete beta function
    Defining formula
    B x ⁡ ( a , b ) incomplete-Beta 𝑥 𝑎 𝑏 {\displaystyle{\displaystyle\mathrm{B}_{\NVar{x}}\left(\NVar{a},\NVar{b}\right% )}}
    xml-id
    C8.S17.E1.m2abdec
    0 references
    Q11360
    Defining formula
    a 𝑎 {\displaystyle{\displaystyle a}}
    xml-id
    C8.S17.XMD1.m1edec
    0 references
    Q11361
    Defining formula
    b 𝑏 {\displaystyle{\displaystyle b}}
    xml-id
    C8.S17.XMD2.m1ddec
    0 references
    Q11362
    Defining formula
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C8.S17.XMD3.m1edec
    0 references
     
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