DLMF:17.5.E1 (Q5363): Difference between revisions

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‎Changed an Item: Add constraint
‎Changed an Item: Add constraint
Property / Symbols used
 
Property / Symbols used: Q10754 / rank
 
Normal rank
Property / Symbols used: Q10754 / qualifier
 
Defining formula:

( m n ) binomial 𝑚 𝑛 {\displaystyle{\displaystyle\genfrac{(}{)}{0.0pt}{}{\NVar{m}}{\NVar{n}}}}

\binom{\NVar{m}}{\NVar{n}}
Property / Symbols used: Q10754 / qualifier
 
xml-id: C1.S2.SS1.m1adec

Revision as of 14:56, 2 January 2020

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DLMF:17.5.E1
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    Statements

    Defining formula
    ϕ 0 0 ⁡ ( - ; - ; q , z ) = ∑ n = 0 ∞ ( - 1 ) n ⁢ q ( n 2 ) ⁢ z n ( q ; q ) n = ( z ; q ) ∞ , q-hypergeometric-rphis 0 0 𝑞 𝑧 superscript subscript 𝑛 0 superscript 1 𝑛 superscript 𝑞 binomial 𝑛 2 superscript 𝑧 𝑛 q-Pochhammer-symbol 𝑞 𝑞 𝑛 q-Pochhammer-symbol 𝑧 𝑞 {\displaystyle{\displaystyle{{}_{0}\phi_{0}}\left(-;-;q,z\right)=\sum_{n=0}^{% \infty}\frac{(-1)^{n}q^{\genfrac{(}{)}{0.0pt}{}{n}{2}}z^{n}}{\left(q;q\right)_% {n}}=\left(z;q\right)_{\infty},}}
    0 references
    DLMF id
    DLMF:17.5.E1
    0 references
    constraint
    | z | < 1 𝑧 1 {\displaystyle{\displaystyle|z|<1}}
    0 references
    Symbols used
    Q10754
    Defining formula
    ( m n ) binomial 𝑚 𝑛 {\displaystyle{\displaystyle\genfrac{(}{)}{0.0pt}{}{\NVar{m}}{\NVar{n}}}}
    xml-id
    C1.S2.SS1.m1adec
    0 references
     
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