DLMF:18.20.E9 (Q5851): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Q11125 / rank
 
Normal rank
Property / Symbols used: Q11125 / qualifier
 
test:

F q p ⁡ ( a 1 , … , a p ; b 1 , … , b q ; z ) Gauss-hypergeometric-pFq 𝑝 𝑞 subscript 𝑎 1 … subscript 𝑎 𝑝 subscript 𝑏 1 … subscript 𝑏 𝑞 𝑧 {\displaystyle{\displaystyle{{}_{\NVar{p}}F_{\NVar{q}}}\left(\NVar{a_{1},\dots% ,a_{p}};\NVar{b_{1},\dots,b_{q}};\NVar{z}\right)}}

\genhyperF{\NVar{p}}{\NVar{q}}@{\NVar{a_{1},\dots,a_{p}}}{\NVar{b_{1},\dots,b_{q}}}{\NVar{z}}
Property / Symbols used: Q11125 / qualifier
 
xml-id: C16.S2.m1abdec

Revision as of 00:31, 2 January 2020

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DLMF:18.20.E9
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    Statements

    test
    p n ⁡ ( x ; a , b , a ¯ , b ¯ ) = i n ⁢ ( a + a ¯ ) n ⁢ ( a + b ¯ ) n n ! ⁢ F 2 3 ⁡ ( - n , n + 2 ⁢ ℜ ⁡ ( a + b ) - 1 , a + i ⁢ x a + a ¯ , a + b ¯ ; 1 ) . continuous-Hahn-polynomial-p 𝑛 𝑥 𝑎 𝑏 𝑎 𝑏 imaginary-unit 𝑛 Pochhammer 𝑎 𝑎 𝑛 Pochhammer 𝑎 𝑏 𝑛 𝑛 Gauss-hypergeometric-pFq 3 2 𝑛 𝑛 2 𝑎 𝑏 1 𝑎 imaginary-unit 𝑥 𝑎 𝑎 𝑎 𝑏 1 {\displaystyle{\displaystyle p_{n}\left(x;a,b,\overline{a},\overline{b}\right)% =\frac{{\mathrm{i}^{n}}{\left(a+\overline{a}\right)_{n}}{\left(a+\overline{b}% \right)_{n}}}{n!}\*{{}_{3}F_{2}}\left({-n,n+2\Re(a+b)-1,a+\mathrm{i}x\atop a+% \overline{a},a+\overline{b}};1\right).}}
    0 references
    DLMF id
    DLMF:18.20.E9
    0 references
    Symbols used
    Q11125
    test
    F q p ⁡ ( a 1 , … , a p ; b 1 , … , b q ; z ) Gauss-hypergeometric-pFq 𝑝 𝑞 subscript 𝑎 1 … subscript 𝑎 𝑝 subscript 𝑏 1 … subscript 𝑏 𝑞 𝑧 {\displaystyle{\displaystyle{{}_{\NVar{p}}F_{\NVar{q}}}\left(\NVar{a_{1},\dots% ,a_{p}};\NVar{b_{1},\dots,b_{q}};\NVar{z}\right)}}
    xml-id
    C16.S2.m1abdec
    0 references
     
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