DLMF:18.27.E14 (Q5965): Difference between revisions

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Property / constraint
 

0 < a < q - 1 , b < q - 1 formulae-sequence 0 𝑎 superscript 𝑞 1 𝑏 superscript 𝑞 1 {\displaystyle{\displaystyle 0<a<q^{-1},b<q^{-1}}}

0<a<q^{-1},b<q^{-1}
Property / constraint: 0 < a < q - 1 , b < q - 1 formulae-sequence 0 𝑎 superscript 𝑞 1 𝑏 superscript 𝑞 1 {\displaystyle{\displaystyle 0<a<q^{-1},b<q^{-1}}} / rank
 
Normal rank
Property / Symbols used
 
Property / Symbols used: Q10768 / rank
 
Normal rank
Property / Symbols used: Q10768 / qualifier
 
test:

δ j , k Kronecker 𝑗 𝑘 {\displaystyle{\displaystyle\delta_{\NVar{j},\NVar{k}}}}

\Kroneckerdelta{\NVar{j}}{\NVar{k}}
Property / Symbols used: Q10768 / qualifier
 
xml-id: introduction.Sx4.p1.t1.r4.m5abdec
Property / Symbols used
 
Property / Symbols used: Q11298 / rank
 
Normal rank
Property / Symbols used: Q11298 / qualifier
 
test:

( a ; q ) n q-Pochhammer-symbol 𝑎 𝑞 𝑛 {\displaystyle{\displaystyle\left(\NVar{a};\NVar{q}\right)_{\NVar{n}}}}

\qPochhammer{\NVar{a}}{\NVar{q}}{\NVar{n}}
Property / Symbols used: Q11298 / qualifier
 
xml-id: C17.S2.SS1.p1.m2adec
Property / Symbols used
 
Property / Symbols used: Q11743 / rank
 
Normal rank
Property / Symbols used: Q11743 / qualifier
 
test:

y 𝑦 {\displaystyle{\displaystyle y}}

y
Property / Symbols used: Q11743 / qualifier
 
xml-id: C18.S1.XMD1.m1adec
Property / Symbols used
 
Property / Symbols used: Q11728 / rank
 
Normal rank
Property / Symbols used: Q11728 / qualifier
 
test:

q 𝑞 {\displaystyle{\displaystyle q}}

q
Property / Symbols used: Q11728 / qualifier
 
xml-id: C18.S1.XMD3.m1ldec
Property / Symbols used
 
Property / Symbols used: Q11730 / rank
 
Normal rank
Property / Symbols used: Q11730 / qualifier
 
test:

m 𝑚 {\displaystyle{\displaystyle m}}

m
Property / Symbols used: Q11730 / qualifier
 
xml-id: C18.S1.XMD5.m1bdec
Property / Symbols used
 
Property / Symbols used: Q11726 / rank
 
Normal rank
Property / Symbols used: Q11726 / qualifier
 
test:

n 𝑛 {\displaystyle{\displaystyle n}}

n
Property / Symbols used: Q11726 / qualifier
 
xml-id: C18.S1.XMD6.m1idec
Property / Symbols used
 
Property / Symbols used: Q11731 / rank
 
Normal rank
Property / Symbols used: Q11731 / qualifier
 
test:

p n ⁢ ( x ) subscript 𝑝 𝑛 𝑥 {\displaystyle{\displaystyle p_{n}(x)}}

p_{n}(x)
Property / Symbols used: Q11731 / qualifier
 
xml-id: C18.S1.XMD9.m1edec
Property / Symbols used
 
Property / Symbols used: DLMF:18.2.E5 / rank
 
Normal rank
Property / Symbols used: DLMF:18.2.E5 / qualifier
 
test:

h n subscript ℎ 𝑛 {\displaystyle{\displaystyle h_{n}}}

h_{n}
Property / Symbols used: DLMF:18.2.E5 / qualifier
 
xml-id: C18.S2.XMD4.m1bdec

Latest revision as of 00:49, 2 January 2020

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DLMF:18.27.E14
No description defined

    Statements

    test
    ∑ y = 0 ∞ p n ⁢ ( q y ) ⁢ p m ⁢ ( q y ) ⁢ ( b ⁢ q ; q ) y ⁢ ( a ⁢ q ) y ( q ; q ) y = h n ⁢ δ n , m , superscript subscript 𝑦 0 subscript 𝑝 𝑛 superscript 𝑞 𝑦 subscript 𝑝 𝑚 superscript 𝑞 𝑦 q-Pochhammer-symbol 𝑏 𝑞 𝑞 𝑦 superscript 𝑎 𝑞 𝑦 q-Pochhammer-symbol 𝑞 𝑞 𝑦 subscript ℎ 𝑛 Kronecker 𝑛 𝑚 {\displaystyle{\displaystyle\sum_{y=0}^{\infty}p_{n}(q^{y})p_{m}(q^{y})\frac{% \left(bq;q\right)_{y}(aq)^{y}}{\left(q;q\right)_{y}}=h_{n}\delta_{n,m},}}
    0 references
    DLMF id
    DLMF:18.27.E14
    0 references
    constraint
    0 < a < q - 1 , b < q - 1 formulae-sequence 0 𝑎 superscript 𝑞 1 𝑏 superscript 𝑞 1 {\displaystyle{\displaystyle 0<a<q^{-1},b<q^{-1}}}
    0 references
    Symbols used
    Q10768
    test
    δ j , k Kronecker 𝑗 𝑘 {\displaystyle{\displaystyle\delta_{\NVar{j},\NVar{k}}}}
    xml-id
    introduction.Sx4.p1.t1.r4.m5abdec
    0 references
    Q11298
    test
    ( a ; q ) n q-Pochhammer-symbol 𝑎 𝑞 𝑛 {\displaystyle{\displaystyle\left(\NVar{a};\NVar{q}\right)_{\NVar{n}}}}
    xml-id
    C17.S2.SS1.p1.m2adec
    0 references
    Q11743
    test
    y 𝑦 {\displaystyle{\displaystyle y}}
    xml-id
    C18.S1.XMD1.m1adec
    0 references
    Q11728
    test
    q 𝑞 {\displaystyle{\displaystyle q}}
    xml-id
    C18.S1.XMD3.m1ldec
    0 references
    Q11730
    test
    m 𝑚 {\displaystyle{\displaystyle m}}
    xml-id
    C18.S1.XMD5.m1bdec
    0 references
    Q11726
    test
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C18.S1.XMD6.m1idec
    0 references
    Q11731
    test
    p n ⁢ ( x ) subscript 𝑝 𝑛 𝑥 {\displaystyle{\displaystyle p_{n}(x)}}
    xml-id
    C18.S1.XMD9.m1edec
    0 references
    DLMF:18.2.E5
    test
    h n subscript ℎ 𝑛 {\displaystyle{\displaystyle h_{n}}}
    xml-id
    C18.S2.XMD4.m1bdec
    0 references
     
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