DLMF:15.5.E16 (Q5033): Difference between revisions

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Changed an Item: Add constraint
Changed an Item: Add constraint
Property / Symbols used
 
Property / Symbols used: Q11645 / rank
 
Normal rank
Property / Symbols used: Q11645 / qualifier
 
Defining formula:

a 𝑎 {\displaystyle{\displaystyle a}}

a
Property / Symbols used: Q11645 / qualifier
 
xml-id: C15.S1.XMD4.m1ndec

Revision as of 13:55, 2 January 2020

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DLMF:15.5.E16
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    Statements

    c ( 1 - z ) F ( a , b ; c ; z ) - c F ( a - 1 , b ; c ; z ) + ( c - b ) z F ( a , b ; c + 1 ; z ) = 0 , 𝑐 1 𝑧 Gauss-hypergeometric-F 𝑎 𝑏 𝑐 𝑧 𝑐 Gauss-hypergeometric-F 𝑎 1 𝑏 𝑐 𝑧 𝑐 𝑏 𝑧 Gauss-hypergeometric-F 𝑎 𝑏 𝑐 1 𝑧 0 {\displaystyle{\displaystyle c(1-z)F\left(a,b;c;z\right)-cF\left(a-1,b;c;z% \right)+(c-b)zF\left(a,b;c+1;z\right)=0,}}
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    DLMF:15.5.E16
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    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)}}
    C15.S2.E1.m2andec
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    z 𝑧 {\displaystyle{\displaystyle z}}
    C15.S1.XMD3.m1odec
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    a 𝑎 {\displaystyle{\displaystyle a}}
    C15.S1.XMD4.m1ndec
    0 references