DLMF:15.5.E6 (Q5023): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Q10759 / rank
 
Normal rank
Property / Symbols used: Q10759 / qualifier
 
Defining formula:

( a ) n Pochhammer 𝑎 𝑛 {\displaystyle{\displaystyle{\left(\NVar{a}\right)_{\NVar{n}}}}}

\Pochhammersym{\NVar{a}}{\NVar{n}}
Property / Symbols used: Q10759 / qualifier
 
xml-id: C5.S2.SS3.m1addec

Revision as of 13:53, 2 January 2020

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DLMF:15.5.E6
No description defined

    Statements

    Defining formula
    d n d z n ⁡ ( ( 1 - z ) a + b - c ⁢ F ⁡ ( a , b ; c ; z ) ) = ( c - a ) n ⁢ ( c - b ) n ( c ) n ⁢ ( 1 - z ) a + b - c - n ⁢ F ⁡ ( a , b ; c + n ; z ) . derivative 𝑧 𝑛 superscript 1 𝑧 𝑎 𝑏 𝑐 Gauss-hypergeometric-F 𝑎 𝑏 𝑐 𝑧 Pochhammer 𝑐 𝑎 𝑛 Pochhammer 𝑐 𝑏 𝑛 Pochhammer 𝑐 𝑛 superscript 1 𝑧 𝑎 𝑏 𝑐 𝑛 Gauss-hypergeometric-F 𝑎 𝑏 𝑐 𝑛 𝑧 {\displaystyle{\displaystyle\frac{{\mathrm{d}}^{n}}{{\mathrm{d}z}^{n}}\left((1% -z)^{a+b-c}F\left(a,b;c;z\right)\right)=\frac{{\left(c-a\right)_{n}}{\left(c-b% \right)_{n}}}{{\left(c\right)_{n}}}(1-z)^{a+b-c-n}\*F\left(a,b;c+n;z\right).}}
    0 references
    DLMF id
    DLMF:15.5.E6
    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.m2aedec
    0 references
    Q10759
    Defining formula
    ( a ) n Pochhammer 𝑎 𝑛 {\displaystyle{\displaystyle{\left(\NVar{a}\right)_{\NVar{n}}}}}
    xml-id
    C5.S2.SS3.m1addec
    0 references
     
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