DLMF:15.5.E1 (Q5018): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: $$={{}_{2}F_{1}}\left(\NVar{a},\NVar{b};\NVar{c};\NVar{z}\right)$$ Gauss’ hypergeometric function / rank
 
Normal rank
Property / Symbols used: $$={{}_{2}F_{1}}\left(\NVar{a},\NVar{b};\NVar{c};\NVar{z}\right)$$ Gauss’ hypergeometric function / qualifier
 
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)}}

\hyperF@{\NVar{a}}{\NVar{b}}{\NVar{c}}{\NVar{z}}
Property / Symbols used: $$={{}_{2}F_{1}}\left(\NVar{a},\NVar{b};\NVar{c};\NVar{z}\right)$$ Gauss’ hypergeometric function / qualifier
 
xml-id: C15.S2.E1.m2adec

Revision as of 13:51, 2 January 2020

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DLMF:15.5.E1
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    Statements

    Defining formula
    d d z ⁡ F ⁡ ( a , b ; c ; z ) = a ⁢ b c ⁢ F ⁡ ( a + 1 , b + 1 ; c + 1 ; z ) , derivative 𝑧 Gauss-hypergeometric-F 𝑎 𝑏 𝑐 𝑧 𝑎 𝑏 𝑐 Gauss-hypergeometric-F 𝑎 1 𝑏 1 𝑐 1 𝑧 {\displaystyle{\displaystyle\frac{\mathrm{d}}{\mathrm{d}z}F\left(a,b;c;z\right% )=\frac{ab}{c}F\left(a+1,b+1;c+1;z\right),}}
    0 references
    DLMF id
    DLMF:15.5.E1
    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
     
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