DLMF:18.27.E6 (Q5957): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Q11713 / rank
 
Normal rank
Property / Symbols used: Q11713 / qualifier
 
Defining formula:

( a 1 , a 2 , … , a r ; q ) n q-multiple-Pochhammer subscript 𝑎 1 subscript 𝑎 2 … subscript 𝑎 𝑟 𝑞 𝑛 {\displaystyle{\displaystyle\left(\NVar{a_{1},a_{2},\dots,a_{r}};\NVar{q}% \right)_{\NVar{n}}}}

\qmultiPochhammersym{\NVar{a_{1},a_{2},\dots,a_{r}}}{\NVar{q}}{\NVar{n}}
Property / Symbols used: Q11713 / qualifier
 
xml-id: C17.S2.SS1.p1.m6adec
Property / Symbols used
 
Property / Symbols used: Q11728 / rank
 
Normal rank
Property / Symbols used: Q11728 / qualifier
 
Defining formula:

q 𝑞 {\displaystyle{\displaystyle q}}

q
Property / Symbols used: Q11728 / qualifier
 
xml-id: C18.S1.XMD3.m1ddec
Property / Symbols used
 
Property / Symbols used: Q11726 / rank
 
Normal rank
Property / Symbols used: Q11726 / qualifier
 
Defining formula:

n 𝑛 {\displaystyle{\displaystyle n}}

n
Property / Symbols used: Q11726 / qualifier
 
xml-id: C18.S1.XMD6.m1edec
Property / Symbols used
 
Property / Symbols used: Q11727 / rank
 
Normal rank
Property / Symbols used: Q11727 / qualifier
 
Defining formula:

x 𝑥 {\displaystyle{\displaystyle x}}

x
Property / Symbols used: Q11727 / qualifier
 
xml-id: C18.S2.XMD3.m1ddec

Latest revision as of 01:48, 2 January 2020

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DLMF:18.27.E6
No description defined

    Statements

    Defining formula
    P n ( α , β ) ⁡ ( x ; c , d ; q ) = c n ⁢ q - ( α + 1 ) ⁢ n ⁢ ( q α + 1 , - q α + 1 ⁢ c - 1 ⁢ d ; q ) n ( q , - q ; q ) n ⁢ P n ⁡ ( q α + 1 ⁢ c - 1 ⁢ x ; q α , q β , - q α ⁢ c - 1 ⁢ d ; q ) . big-q-Jacobi-polynomial-P-type-2 𝛼 𝛽 𝑛 𝑥 𝑐 𝑑 𝑞 superscript 𝑐 𝑛 superscript 𝑞 𝛼 1 𝑛 q-multiple-Pochhammer superscript 𝑞 𝛼 1 superscript 𝑞 𝛼 1 superscript 𝑐 1 𝑑 𝑞 𝑛 q-multiple-Pochhammer 𝑞 𝑞 𝑞 𝑛 q-Jacobi-polynomial-P 𝑛 superscript 𝑞 𝛼 1 superscript 𝑐 1 𝑥 superscript 𝑞 𝛼 superscript 𝑞 𝛽 superscript 𝑞 𝛼 superscript 𝑐 1 𝑑 𝑞 {\displaystyle{\displaystyle P^{(\alpha,\beta)}_{n}\left(x;c,d;q\right)=\frac{% c^{n}q^{-(\alpha+1)n}\left(q^{\alpha+1},-q^{\alpha+1}c^{-1}d;q\right)_{n}}{% \left(q,-q;q\right)_{n}}\*P_{n}\left(q^{\alpha+1}c^{-1}x;q^{\alpha},q^{\beta},% -q^{\alpha}c^{-1}d;q\right).}}
    0 references
    DLMF id
    DLMF:18.27.E6
    0 references
    Symbols used
    Q10777
    Defining formula
    ( a , b ) 𝑎 𝑏 {\displaystyle{\displaystyle(\NVar{a},\NVar{b})}}
    xml-id
    introduction.Sx4.p1.t1.r29.m6adec
    0 references
    big $$q$$ -Jacobi polynomial
    Defining formula
    P n ⁡ ( x ; a , b , c ; q ) q-Jacobi-polynomial-P 𝑛 𝑥 𝑎 𝑏 𝑐 𝑞 {\displaystyle{\displaystyle P_{\NVar{n}}\left(\NVar{x};\NVar{a},\NVar{b},% \NVar{c};\NVar{q}\right)}}
    xml-id
    C18.S27.E5.m2aadec
    0 references
    Q11713
    Defining formula
    ( a 1 , a 2 , … , a r ; q ) n q-multiple-Pochhammer subscript 𝑎 1 subscript 𝑎 2 … subscript 𝑎 𝑟 𝑞 𝑛 {\displaystyle{\displaystyle\left(\NVar{a_{1},a_{2},\dots,a_{r}};\NVar{q}% \right)_{\NVar{n}}}}
    xml-id
    C17.S2.SS1.p1.m6adec
    0 references
    Q11728
    Defining formula
    q 𝑞 {\displaystyle{\displaystyle q}}
    xml-id
    C18.S1.XMD3.m1ddec
    0 references
    Q11726
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C18.S1.XMD6.m1edec
    0 references
    Q11727
    Defining formula
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C18.S2.XMD3.m1ddec
    0 references
     
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